diff --git a/doc/pub/week35/html/._week35-bs010.html b/doc/pub/week35/html/._week35-bs010.html
index 24461334b..1dceb8be0 100644
--- a/doc/pub/week35/html/._week35-bs010.html
+++ b/doc/pub/week35/html/._week35-bs010.html
@@ -381,10 +381,10 @@ $$
 
 <p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T.
 $$
 
-<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.</p>
 
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index 78deaf60f..894906df6 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -540,11 +540,11 @@ $$
 <p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 <p>&nbsp;<br>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T.
 $$
 <p>&nbsp;<br>
 
-<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.</p>
 
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 <p>&nbsp;<br>
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index 9310fb771..f7139726d 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -604,10 +604,10 @@ $$
 
 <p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T.
 $$
 
-<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.</p>
 
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index 64d36e6e1..f2ade0867 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -681,10 +681,10 @@ $$
 
 <p>which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have</p>
 $$
-\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T=\boldsymbol{A}^T\boldsymbol{y}.
+\frac{\partial \alpha}{\partial \boldsymbol{x}} = \frac{\partial \boldsymbol{z}^T\boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{z}^T.
 $$
 
-<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other.</p>
+<p>Note that the resulting vector elements are the same for \( \boldsymbol{z}^T \) and \( \boldsymbol{z} \), the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.</p>
 
 <p>Since \( \alpha \) is a scalar we have \( \alpha =\alpha^T=\boldsymbol{x}^T\boldsymbol{A}^T\boldsymbol{y} \). Defining now \( \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T \) we find that</p>
 $$
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index 49dc5e02d..dd66d58be 100644
Binary files a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz and b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz differ
diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb
index 7ce405ac8..993730edd 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d1a45cb9",
+   "id": "5e23e311",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df0b160c",
+   "id": "1eaedd60",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5480a93a",
+   "id": "37a2191e",
    "metadata": {
     "editable": true
    },
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d7042d6",
+   "id": "75a3593c",
    "metadata": {
     "editable": true
    },
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f38f6344",
+   "id": "ca72d9e0",
    "metadata": {
     "editable": true
    },
@@ -103,7 +103,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88321305",
+   "id": "d782325f",
    "metadata": {
     "editable": true
    },
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3902f8c",
+   "id": "53f0cd7f",
    "metadata": {
     "editable": true
    },
@@ -131,7 +131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6cc9fd26",
+   "id": "93ef494a",
    "metadata": {
     "editable": true
    },
@@ -141,7 +141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "083c1a6b",
+   "id": "6b51dd18",
    "metadata": {
     "editable": true
    },
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38b6975b",
+   "id": "dad04700",
    "metadata": {
     "editable": true
    },
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a65b0a7",
+   "id": "4ca38b77",
    "metadata": {
     "editable": true
    },
@@ -186,7 +186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7097614a",
+   "id": "d7ff29ea",
    "metadata": {
     "editable": true
    },
@@ -199,7 +199,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d57cdf7e",
+   "id": "12cc22b1",
    "metadata": {
     "editable": true
    },
@@ -211,7 +211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ee5538d",
+   "id": "789edb60",
    "metadata": {
     "editable": true
    },
@@ -223,7 +223,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09ce36b5",
+   "id": "4be56945",
    "metadata": {
     "editable": true
    },
@@ -233,7 +233,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3884daa6",
+   "id": "52ebbe29",
    "metadata": {
     "editable": true
    },
@@ -245,7 +245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "046f3817",
+   "id": "b0573b73",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "327fd863",
+   "id": "80e80d13",
    "metadata": {
     "editable": true
    },
@@ -270,7 +270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2df2b68",
+   "id": "0baee0d9",
    "metadata": {
     "editable": true
    },
@@ -280,7 +280,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5b6d8a1",
+   "id": "241ff2c2",
    "metadata": {
     "editable": true
    },
@@ -292,7 +292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f40f76e8",
+   "id": "1fa75fec",
    "metadata": {
     "editable": true
    },
@@ -304,7 +304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7b515ea",
+   "id": "2d38f4c4",
    "metadata": {
     "editable": true
    },
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "915095bd",
+   "id": "2f88831c",
    "metadata": {
     "editable": true
    },
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1dd8cbd",
+   "id": "a59da092",
    "metadata": {
     "editable": true
    },
@@ -346,7 +346,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1530e93c",
+   "id": "7f2479bc",
    "metadata": {
     "editable": true
    },
@@ -359,7 +359,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e96b563a",
+   "id": "42e31098",
    "metadata": {
     "editable": true
    },
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "982d1604",
+   "id": "030110dc",
    "metadata": {
     "editable": true
    },
@@ -381,7 +381,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32a75225",
+   "id": "6ad48d84",
    "metadata": {
     "editable": true
    },
@@ -391,7 +391,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54f26dca",
+   "id": "3b806c78",
    "metadata": {
     "editable": true
    },
@@ -403,7 +403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4310cf8b",
+   "id": "dfa92293",
    "metadata": {
     "editable": true
    },
@@ -413,7 +413,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f7dd61f",
+   "id": "0946613c",
    "metadata": {
     "editable": true
    },
@@ -425,7 +425,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f18dbba1",
+   "id": "d28e8d9c",
    "metadata": {
     "editable": true
    },
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b6d945a",
+   "id": "4aa55b8c",
    "metadata": {
     "editable": true
    },
@@ -448,7 +448,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a1244bc",
+   "id": "4d8faa25",
    "metadata": {
     "editable": true
    },
@@ -458,7 +458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87368735",
+   "id": "60a816bf",
    "metadata": {
     "editable": true
    },
@@ -470,7 +470,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c9a49592",
+   "id": "10b9b9d3",
    "metadata": {
     "editable": true
    },
@@ -480,7 +480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f2233cd",
+   "id": "4556da08",
    "metadata": {
     "editable": true
    },
@@ -492,7 +492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7393b1df",
+   "id": "684eca57",
    "metadata": {
     "editable": true
    },
@@ -512,7 +512,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16eb1cab",
+   "id": "55ee5ba9",
    "metadata": {
     "editable": true
    },
@@ -539,7 +539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fadb6c5f",
+   "id": "68884f20",
    "metadata": {
     "editable": true
    },
@@ -551,7 +551,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b226a3b",
+   "id": "16e81ebc",
    "metadata": {
     "editable": true
    },
@@ -563,7 +563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8835682a",
+   "id": "eb3f931b",
    "metadata": {
     "editable": true
    },
@@ -579,7 +579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94ea8746",
+   "id": "02ebd138",
    "metadata": {
     "editable": true
    },
@@ -597,7 +597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8a3e5ff",
+   "id": "54a8b752",
    "metadata": {
     "editable": true
    },
@@ -609,7 +609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2aeb647a",
+   "id": "a2215462",
    "metadata": {
     "editable": true
    },
@@ -621,7 +621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1a9041d",
+   "id": "fafd6d4d",
    "metadata": {
     "editable": true
    },
@@ -632,7 +632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d68af48",
+   "id": "f425548e",
    "metadata": {
     "editable": true
    },
@@ -644,7 +644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f16856a",
+   "id": "083e1ef6",
    "metadata": {
     "editable": true
    },
@@ -654,7 +654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b5f1f53",
+   "id": "b9a6a35f",
    "metadata": {
     "editable": true
    },
@@ -666,7 +666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdc1e2de",
+   "id": "e78c1c87",
    "metadata": {
     "editable": true
    },
@@ -680,7 +680,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2d5e2ac",
+   "id": "92e111b6",
    "metadata": {
     "editable": true
    },
@@ -692,7 +692,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6100c9ac",
+   "id": "caa38542",
    "metadata": {
     "editable": true
    },
@@ -704,7 +704,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4ca2a6c",
+   "id": "d5ba390d",
    "metadata": {
     "editable": true
    },
@@ -716,7 +716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7af8ed53",
+   "id": "591056e0",
    "metadata": {
     "editable": true
    },
@@ -726,31 +726,31 @@
   },
   {
    "cell_type": "markdown",
-   "id": "969a360f",
+   "id": "23dc6906",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\frac{\\partial \\boldsymbol{z}^T\\boldsymbol{x}}{\\partial \\boldsymbol{x}}=\\boldsymbol{z}^T=\\boldsymbol{A}^T\\boldsymbol{y}.\n",
+    "\\frac{\\partial \\alpha}{\\partial \\boldsymbol{x}} = \\frac{\\partial \\boldsymbol{z}^T\\boldsymbol{x}}{\\partial \\boldsymbol{x}}=\\boldsymbol{z}^T.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bb94df46",
+   "id": "86c5aa25",
    "metadata": {
     "editable": true
    },
    "source": [
-    "Note that the resulting vector elements are the same for $\\boldsymbol{z}^T$ and $\\boldsymbol{z}$, the only difference is that one is just the transpose of the other.\n",
+    "Note that the resulting vector elements are the same for $\\boldsymbol{z}^T$ and $\\boldsymbol{z}$, the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.\n",
     "\n",
     "Since $\\alpha$ is a scalar we have $\\alpha =\\alpha^T=\\boldsymbol{x}^T\\boldsymbol{A}^T\\boldsymbol{y}$. Defining now $\\boldsymbol{z}^T=\\boldsymbol{x}^T\\boldsymbol{A}^T$ we find that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6415e688",
+   "id": "7dda247d",
    "metadata": {
     "editable": true
    },
@@ -762,7 +762,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b3b1ecd",
+   "id": "09003774",
    "metadata": {
     "editable": true
    },
@@ -776,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a986474a",
+   "id": "2a4f5a8a",
    "metadata": {
     "editable": true
    },
@@ -788,7 +788,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af874fe9",
+   "id": "4e5a341e",
    "metadata": {
     "editable": true
    },
@@ -800,7 +800,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "074b1322",
+   "id": "7c1f4e32",
    "metadata": {
     "editable": true
    },
@@ -812,7 +812,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8120e11",
+   "id": "a4ff9f0e",
    "metadata": {
     "editable": true
    },
@@ -822,7 +822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c4a9f64",
+   "id": "27dc6035",
    "metadata": {
     "editable": true
    },
@@ -834,7 +834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a99ee98",
+   "id": "0021162f",
    "metadata": {
     "editable": true
    },
@@ -844,7 +844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4d80443",
+   "id": "bf92f77b",
    "metadata": {
     "editable": true
    },
@@ -856,7 +856,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8faa132f",
+   "id": "05af4551",
    "metadata": {
     "editable": true
    },
@@ -866,7 +866,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cbb38e2d",
+   "id": "a8d65fe5",
    "metadata": {
     "editable": true
    },
@@ -878,7 +878,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c57d10e0",
+   "id": "c25c9f96",
    "metadata": {
     "editable": true
    },
@@ -890,7 +890,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7acf1bc0",
+   "id": "f0a93dca",
    "metadata": {
     "editable": true
    },
@@ -902,7 +902,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0268eb52",
+   "id": "cf3cae66",
    "metadata": {
     "editable": true
    },
@@ -917,7 +917,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60003495",
+   "id": "fca6b233",
    "metadata": {
     "editable": true
    },
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87737af5",
+   "id": "6df15694",
    "metadata": {
     "editable": true
    },
@@ -939,7 +939,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "172d2360",
+   "id": "7dc52af7",
    "metadata": {
     "editable": true
    },
@@ -951,7 +951,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c8b553e",
+   "id": "580f500f",
    "metadata": {
     "editable": true
    },
@@ -961,7 +961,7 @@
   },
   {
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@@ -973,7 +973,7 @@
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@@ -983,7 +983,7 @@
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@@ -995,7 +995,7 @@
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@@ -1007,7 +1007,7 @@
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@@ -1019,7 +1019,7 @@
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@@ -1029,7 +1029,7 @@
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@@ -1041,7 +1041,7 @@
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@@ -1054,7 +1054,7 @@
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@@ -1066,7 +1066,7 @@
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@@ -1076,7 +1076,7 @@
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@@ -1088,7 +1088,7 @@
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@@ -1098,7 +1098,7 @@
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@@ -1110,7 +1110,7 @@
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@@ -1120,7 +1120,7 @@
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@@ -1132,7 +1132,7 @@
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@@ -1142,7 +1142,7 @@
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@@ -1154,7 +1154,7 @@
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@@ -1164,7 +1164,7 @@
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@@ -1176,7 +1176,7 @@
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@@ -1188,7 +1188,7 @@
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@@ -1200,7 +1200,7 @@
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@@ -1212,7 +1212,7 @@
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@@ -1224,7 +1224,7 @@
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@@ -1236,7 +1236,7 @@
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@@ -1252,7 +1252,7 @@
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@@ -1264,7 +1264,7 @@
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@@ -1274,7 +1274,7 @@
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@@ -1286,7 +1286,7 @@
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@@ -1304,7 +1304,7 @@
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@@ -1316,7 +1316,7 @@
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@@ -1328,7 +1328,7 @@
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@@ -1338,7 +1338,7 @@
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@@ -1350,7 +1350,7 @@
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@@ -1360,7 +1360,7 @@
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@@ -1372,7 +1372,7 @@
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@@ -1382,7 +1382,7 @@
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@@ -1396,7 +1396,7 @@
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@@ -1408,7 +1408,7 @@
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@@ -1419,7 +1419,7 @@
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@@ -1432,7 +1432,7 @@
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@@ -1459,7 +1459,7 @@
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@@ -1470,7 +1470,7 @@
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@@ -1483,7 +1483,7 @@
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@@ -1497,7 +1497,7 @@
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@@ -1510,7 +1510,7 @@
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@@ -1521,7 +1521,7 @@
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@@ -1533,7 +1533,7 @@
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@@ -1544,7 +1544,7 @@
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@@ -1560,7 +1560,7 @@
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@@ -1571,7 +1571,7 @@
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@@ -1585,7 +1585,7 @@
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@@ -1606,7 +1606,7 @@
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@@ -1617,7 +1617,7 @@
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@@ -1670,7 +1670,7 @@
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@@ -1681,7 +1681,7 @@
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@@ -1706,7 +1706,7 @@
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@@ -1718,7 +1718,7 @@
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@@ -1747,7 +1747,7 @@
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@@ -1772,7 +1772,7 @@
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@@ -1792,7 +1792,7 @@
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@@ -1819,7 +1819,7 @@
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@@ -1832,7 +1832,7 @@
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@@ -1844,7 +1844,7 @@
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@@ -1855,7 +1855,7 @@
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@@ -1871,7 +1871,7 @@
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@@ -1905,7 +1905,7 @@
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@@ -1915,7 +1915,7 @@
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@@ -1930,7 +1930,7 @@
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@@ -1942,7 +1942,7 @@
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@@ -1952,7 +1952,7 @@
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@@ -1968,7 +1968,7 @@
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@@ -1985,7 +1985,7 @@
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@@ -1998,7 +1998,7 @@
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@@ -2045,7 +2045,7 @@
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@@ -2056,7 +2056,7 @@
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@@ -2159,7 +2159,7 @@
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@@ -2187,7 +2187,7 @@
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@@ -2222,7 +2222,7 @@
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@@ -2237,7 +2237,7 @@
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@@ -2262,7 +2262,7 @@
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@@ -2278,7 +2278,7 @@
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@@ -2290,7 +2290,7 @@
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@@ -2305,7 +2305,7 @@
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@@ -2317,7 +2317,7 @@
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@@ -2327,7 +2327,7 @@
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@@ -2339,7 +2339,7 @@
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@@ -2349,7 +2349,7 @@
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@@ -2361,7 +2361,7 @@
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@@ -2374,7 +2374,7 @@
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@@ -2386,7 +2386,7 @@
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@@ -2396,7 +2396,7 @@
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@@ -2408,7 +2408,7 @@
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@@ -2418,7 +2418,7 @@
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@@ -2430,7 +2430,7 @@
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@@ -2440,7 +2440,7 @@
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@@ -2452,7 +2452,7 @@
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@@ -2462,7 +2462,7 @@
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@@ -2474,7 +2474,7 @@
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@@ -2484,7 +2484,7 @@
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@@ -2496,7 +2496,7 @@
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@@ -2506,7 +2506,7 @@
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@@ -2518,7 +2518,7 @@
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@@ -2530,7 +2530,7 @@
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@@ -2542,7 +2542,7 @@
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@@ -2555,7 +2555,7 @@
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@@ -2567,7 +2567,7 @@
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@@ -2577,7 +2577,7 @@
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@@ -2591,7 +2591,7 @@
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@@ -2688,7 +2688,7 @@
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@@ -2709,7 +2709,7 @@
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@@ -2721,7 +2721,7 @@
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@@ -2731,7 +2731,7 @@
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@@ -2743,7 +2743,7 @@
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@@ -2753,7 +2753,7 @@
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@@ -2765,7 +2765,7 @@
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@@ -2781,7 +2781,7 @@
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@@ -2791,7 +2791,7 @@
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@@ -2805,7 +2805,7 @@
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@@ -2817,7 +2817,7 @@
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@@ -2829,7 +2829,7 @@
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@@ -2841,7 +2841,7 @@
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@@ -2851,7 +2851,7 @@
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@@ -2863,7 +2863,7 @@
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@@ -2873,7 +2873,7 @@
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@@ -2885,7 +2885,7 @@
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@@ -2896,7 +2896,7 @@
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@@ -2908,7 +2908,7 @@
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@@ -2920,7 +2920,7 @@
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@@ -2930,7 +2930,7 @@
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@@ -2942,7 +2942,7 @@
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@@ -2954,7 +2954,7 @@
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@@ -2964,7 +2964,7 @@
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@@ -2976,7 +2976,7 @@
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@@ -2986,7 +2986,7 @@
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@@ -2998,7 +2998,7 @@
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@@ -3008,7 +3008,7 @@
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@@ -3048,7 +3048,7 @@
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@@ -3065,7 +3065,7 @@
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@@ -3088,7 +3088,7 @@
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@@ -3105,7 +3105,7 @@
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@@ -3124,7 +3124,7 @@
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@@ -3135,7 +3135,7 @@
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@@ -3147,7 +3147,7 @@
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@@ -3165,7 +3165,7 @@
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@@ -3181,7 +3181,7 @@
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@@ -3193,7 +3193,7 @@
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@@ -3203,7 +3203,7 @@
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@@ -3218,7 +3218,7 @@
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@@ -3230,7 +3230,7 @@
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@@ -3240,7 +3240,7 @@
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@@ -3252,7 +3252,7 @@
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@@ -3262,7 +3262,7 @@
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@@ -3274,7 +3274,7 @@
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@@ -3286,7 +3286,7 @@
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@@ -3301,7 +3301,7 @@
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@@ -3312,7 +3312,7 @@
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@@ -3332,7 +3332,7 @@
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@@ -3344,7 +3344,7 @@
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@@ -3354,7 +3354,7 @@
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@@ -3366,7 +3366,7 @@
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@@ -3395,7 +3395,7 @@
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@@ -3422,7 +3422,7 @@
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@@ -3433,7 +3433,7 @@
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@@ -3473,7 +3473,7 @@
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@@ -3490,7 +3490,7 @@
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@@ -3513,7 +3513,7 @@
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@@ -3527,7 +3527,7 @@
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@@ -3546,7 +3546,7 @@
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@@ -3556,7 +3556,7 @@
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@@ -3568,7 +3568,7 @@
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@@ -3582,7 +3582,7 @@
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@@ -3594,7 +3594,7 @@
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@@ -3604,7 +3604,7 @@
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@@ -3616,7 +3616,7 @@
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@@ -3633,7 +3633,7 @@
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@@ -3643,7 +3643,7 @@
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@@ -3659,7 +3659,7 @@
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@@ -3669,7 +3669,7 @@
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@@ -3685,7 +3685,7 @@
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@@ -3695,7 +3695,7 @@
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@@ -3711,7 +3711,7 @@
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@@ -3721,7 +3721,7 @@
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@@ -3738,7 +3738,7 @@
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@@ -3750,7 +3750,7 @@
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@@ -3762,7 +3762,7 @@
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@@ -3774,7 +3774,7 @@
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@@ -3784,7 +3784,7 @@
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@@ -3796,7 +3796,7 @@
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@@ -3808,7 +3808,7 @@
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@@ -3820,7 +3820,7 @@
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@@ -3830,7 +3830,7 @@
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@@ -3842,7 +3842,7 @@
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@@ -3852,7 +3852,7 @@
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@@ -3864,7 +3864,7 @@
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@@ -3880,7 +3880,7 @@
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@@ -3892,7 +3892,7 @@
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@@ -3904,7 +3904,7 @@
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@@ -3914,7 +3914,7 @@
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@@ -3926,7 +3926,7 @@
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@@ -3937,7 +3937,7 @@
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@@ -3949,7 +3949,7 @@
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@@ -3959,7 +3959,7 @@
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@@ -3971,7 +3971,7 @@
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@@ -3981,7 +3981,7 @@
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@@ -3993,7 +3993,7 @@
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@@ -4004,7 +4004,7 @@
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@@ -4016,7 +4016,7 @@
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@@ -4034,7 +4034,7 @@
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@@ -4050,7 +4050,7 @@
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@@ -4062,7 +4062,7 @@
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@@ -4074,7 +4074,7 @@
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@@ -4086,7 +4086,7 @@
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@@ -4099,7 +4099,7 @@
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@@ -4115,7 +4115,7 @@
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@@ -4129,7 +4129,7 @@
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@@ -4139,7 +4139,7 @@
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@@ -4151,7 +4151,7 @@
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@@ -4161,7 +4161,7 @@
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@@ -4173,7 +4173,7 @@
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@@ -4183,7 +4183,7 @@
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@@ -4197,7 +4197,7 @@
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@@ -4214,7 +4214,7 @@
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@@ -4230,7 +4230,7 @@
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@@ -4242,7 +4242,7 @@
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@@ -4255,7 +4255,7 @@
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@@ -4269,7 +4269,7 @@
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@@ -4279,7 +4279,7 @@
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@@ -4292,7 +4292,7 @@
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@@ -4311,7 +4311,7 @@
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@@ -4323,7 +4323,7 @@
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@@ -4335,7 +4335,7 @@
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@@ -4345,7 +4345,7 @@
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@@ -4357,7 +4357,7 @@
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@@ -4370,7 +4370,7 @@
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@@ -4389,7 +4389,7 @@
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@@ -4399,7 +4399,7 @@
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@@ -4418,7 +4418,7 @@
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@@ -4436,7 +4436,7 @@
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@@ -4450,7 +4450,7 @@
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@@ -4465,7 +4465,7 @@
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@@ -4486,7 +4486,7 @@
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@@ -4503,7 +4503,7 @@
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@@ -4535,7 +4535,7 @@
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@@ -4549,7 +4549,7 @@
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@@ -4562,7 +4562,7 @@
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@@ -4587,7 +4587,7 @@
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@@ -4597,7 +4597,7 @@
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@@ -4608,7 +4608,7 @@
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@@ -4662,7 +4662,7 @@
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@@ -4679,7 +4679,7 @@
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@@ -4691,7 +4691,7 @@
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@@ -4703,7 +4703,7 @@
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@@ -4713,7 +4713,7 @@
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@@ -4730,7 +4730,7 @@
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@@ -4740,7 +4740,7 @@
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@@ -4755,7 +4755,7 @@
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@@ -4765,7 +4765,7 @@
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@@ -4779,7 +4779,7 @@
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@@ -4791,7 +4791,7 @@
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@@ -4803,7 +4803,7 @@
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@@ -4815,7 +4815,7 @@
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@@ -4825,7 +4825,7 @@
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@@ -4837,7 +4837,7 @@
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@@ -4847,7 +4847,7 @@
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@@ -4864,7 +4864,7 @@
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@@ -4874,7 +4874,7 @@
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@@ -4886,7 +4886,7 @@
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@@ -4896,7 +4896,7 @@
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@@ -4908,7 +4908,7 @@
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@@ -4922,7 +4922,7 @@
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@@ -4934,7 +4934,7 @@
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@@ -4956,7 +4956,7 @@
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@@ -4968,7 +4968,7 @@
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@@ -4983,7 +4983,7 @@
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@@ -4995,7 +4995,7 @@
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@@ -5007,7 +5007,7 @@
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@@ -5017,7 +5017,7 @@
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@@ -5029,7 +5029,7 @@
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@@ -5039,7 +5039,7 @@
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@@ -5051,7 +5051,7 @@
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@@ -5061,7 +5061,7 @@
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@@ -5073,7 +5073,7 @@
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@@ -5090,7 +5090,7 @@
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@@ -5103,7 +5103,7 @@
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@@ -5115,7 +5115,7 @@
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@@ -5125,7 +5125,7 @@
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@@ -5138,7 +5138,7 @@
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@@ -5148,7 +5148,7 @@
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@@ -5160,7 +5160,7 @@
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@@ -5173,7 +5173,7 @@
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@@ -5186,7 +5186,7 @@
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@@ -5198,7 +5198,7 @@
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@@ -5210,7 +5210,7 @@
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@@ -5220,7 +5220,7 @@
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@@ -5233,7 +5233,7 @@
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@@ -5245,7 +5245,7 @@
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@@ -5257,7 +5257,7 @@
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@@ -5269,7 +5269,7 @@
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@@ -5281,7 +5281,7 @@
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@@ -5295,7 +5295,7 @@
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@@ -5307,7 +5307,7 @@
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@@ -5317,7 +5317,7 @@
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@@ -5329,7 +5329,7 @@
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@@ -5341,7 +5341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45a67a1a",
+   "id": "817c263c",
    "metadata": {
     "editable": true
    },
@@ -5353,7 +5353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efe0de6c",
+   "id": "07a52036",
    "metadata": {
     "editable": true
    },
@@ -5365,7 +5365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8860fc43",
+   "id": "c6a7957f",
    "metadata": {
     "editable": true
    },
@@ -5377,7 +5377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b14ec49",
+   "id": "920e985a",
    "metadata": {
     "editable": true
    },
@@ -5396,7 +5396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa58f8d1",
+   "id": "ad54c88f",
    "metadata": {
     "editable": true
    },
@@ -5408,7 +5408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "848a33e8",
+   "id": "ac1adab6",
    "metadata": {
     "editable": true
    },
@@ -5418,7 +5418,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45cbaee4",
+   "id": "79ebd982",
    "metadata": {
     "editable": true
    },
@@ -5430,7 +5430,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c691de3f",
+   "id": "d66680fb",
    "metadata": {
     "editable": true
    },
@@ -5440,7 +5440,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7e337f4",
+   "id": "9bfaac82",
    "metadata": {
     "editable": true
    },
@@ -5452,7 +5452,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d417ae8",
+   "id": "f3674708",
    "metadata": {
     "editable": true
    },
@@ -5464,7 +5464,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "386aa637",
+   "id": "3c120e3c",
    "metadata": {
     "editable": true
    },
@@ -5480,7 +5480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55185be4",
+   "id": "8c7de2f8",
    "metadata": {
     "editable": true
    },
@@ -5492,7 +5492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a7fcef6",
+   "id": "ebfd01bc",
    "metadata": {
     "editable": true
    },
@@ -5504,7 +5504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f2c4c1d",
+   "id": "3b6ea52b",
    "metadata": {
     "editable": true
    },
@@ -5514,7 +5514,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3bab558",
+   "id": "81ea0e5c",
    "metadata": {
     "editable": true
    },
@@ -5526,7 +5526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb50e5e7",
+   "id": "c13a1ef8",
    "metadata": {
     "editable": true
    },
@@ -5536,7 +5536,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e1bf6c6",
+   "id": "cac609fc",
    "metadata": {
     "editable": true
    },
@@ -5548,7 +5548,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6089b625",
+   "id": "f84092f4",
    "metadata": {
     "editable": true
    },
@@ -5565,7 +5565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68df3751",
+   "id": "a9fc125a",
    "metadata": {
     "editable": true
    },
@@ -5577,7 +5577,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60e8783d",
+   "id": "ee3d9733",
    "metadata": {
     "editable": true
    },
@@ -5589,7 +5589,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75eaf332",
+   "id": "81bc0a7d",
    "metadata": {
     "editable": true
    },
@@ -5599,7 +5599,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98940a5",
+   "id": "31498142",
    "metadata": {
     "editable": true
    },
@@ -5611,7 +5611,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a2a3500",
+   "id": "21c42390",
    "metadata": {
     "editable": true
    },
@@ -5621,7 +5621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea6ff87d",
+   "id": "f08bb4ce",
    "metadata": {
     "editable": true
    },
@@ -5633,7 +5633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb7270da",
+   "id": "98eaed7c",
    "metadata": {
     "editable": true
    },
@@ -5643,7 +5643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1626b163",
+   "id": "f1472525",
    "metadata": {
     "editable": true
    },
@@ -5655,7 +5655,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5182459c",
+   "id": "70d37bf5",
    "metadata": {
     "editable": true
    },
@@ -5665,7 +5665,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "951dec6f",
+   "id": "f8816ccc",
    "metadata": {
     "editable": true
    },
@@ -5677,7 +5677,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f09e051d",
+   "id": "de17f9db",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index 0b0255015..c94075211 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -318,11 +318,11 @@ $\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then, using the defin
 which means that (using our previous example and keeping track of our definition of the derivative of a scalar) we have
 !bt
 \[
-\frac{\partial \alpha}{\partial \bm{x}} = \frac{\partial \bm{z}^T\bm{x}}{\partial \bm{x}}=\bm{z}^T=\bm{A}^T\bm{y}.
+\frac{\partial \alpha}{\partial \bm{x}} = \frac{\partial \bm{z}^T\bm{x}}{\partial \bm{x}}=\bm{z}^T.
 \]
 !et
 
-Note that the resulting vector elements are the same for $\bm{z}^T$ and $\bm{z}$, the only difference is that one is just the transpose of the other.
+Note that the resulting vector elements are the same for $\bm{z}^T$ and $\bm{z}$, the only difference is that one is just the transpose of the other. We have the transposed here since we have used that the inner product of two vectors is a scalar.
 
 Since $\alpha$ is a scalar we have $\alpha =\alpha^T=\bm{x}^T\bm{A}^T\bm{y}$. Defining now $\bm{z}^T=\bm{x}^T\bm{A}^T$ we find that
 !bt