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jkostiuk merged 2 commits into from
May 12, 2026
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Chapter 5 tweaks #1030

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Section 5.1
siwelwerd May 12, 2026
7b00623
Typo
siwelwerd May 12, 2026
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10 changes: 5 additions & 5 deletions source/linear-algebra/source/05-GT/01.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -158,7 +158,7 @@ What is the area of the transformed unit square?
<me>B\vec e_1=\left[\begin{array}{cc} 2 &amp; 3 \\ 0 &amp; 4 \end{array}\right]\left[\begin{array}{c}1\\0\end{array}\right]
=\left[\begin{array}{c}2\\0\end{array}\right]=2\vec e_1</me>

<me>
<me>\def\arraystretch{1.25}
B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]
=
\left[\begin{array}{cc} 2 &amp; 3 \\ 0 &amp; 4 \end{array}\right]\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]
Expand All @@ -175,7 +175,7 @@ What is the area of the transformed unit square?
\draw[thin,gray,&lt;-&gt;] (-4,0)-- (4,0);
\draw[thin,gray,&lt;-&gt;] (0,-4)-- (0,4);
\draw[thick,blue,-&gt;] (0,0) -- node[below] {\(B\left[\begin{array}{c}1\\0\end{array}\right]=2\left[\begin{array}{c}1\\0\end{array}\right]\)}++ (2,0);
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(\def\arraystretch{1.25} B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,red,-&gt;] (0,0) -- (1,0);
\draw[thick,red,-&gt;] (0,0) -- (0.75,0.5);
\draw[red,dashed] (1,0) -- (1.75,0.5) -- (0.75,0.5);
Expand Down Expand Up @@ -228,7 +228,7 @@ What is the area of the transformed unit square?
\draw[thin,gray,&lt;-&gt;] (-4,0)-- (4,0);
\draw[thin,gray,&lt;-&gt;] (0,-4)-- (0,4);
\draw[thick,blue,-&gt;] (0,0) -- node[below] {\(B\left[\begin{array}{c}1\\0\end{array}\right]=2\left[\begin{array}{c}1\\0\end{array}\right]\)}++ (2,0);
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(\def\arraystretch{1.25} B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,red,-&gt;] (0,0) -- (1,0);
\draw[thick,red,-&gt;] (0,0) -- (0.75,0.5);
\draw[red,dashed] (1,0) -- (1.75,0.5) -- (0.75,0.5);
Expand Down Expand Up @@ -275,7 +275,7 @@ In order to figure out how to compute it, we first figure out the properties it
\draw[thin,gray,&lt;-&gt;] (-4,0)-- (4,0);
\draw[thin,gray,&lt;-&gt;] (0,-4)-- (0,4);
\draw[thick,blue,-&gt;] (0,0) -- node[below] {\(B\left[\begin{array}{c}1\\0\end{array}\right]=2\left[\begin{array}{c}1\\0\end{array}\right]\)}++ (2,0);
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,blue,-&gt;] (0,0) -- ++(3,2) node[above] {\(\def\arraystretch{1.25} B\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]=4\left[\begin{array}{c}\frac{3}{4}\\\frac{1}{2}\end{array}\right]\)};
\draw[thick,red,-&gt;] (0,0) -- (1,0);
\draw[thick,red,-&gt;] (0,0) -- (0.75,0.5);
\draw[red,dashed] (1,0) -- (1.75,0.5) -- (0.75,0.5);
Expand All @@ -301,7 +301,7 @@ If <m>\det([\vec{e}_1\hspace{0.5em} \vec{e}_2])=\det(I)</m> is the
area of resulting parallelogram, what is the value of <m>\det([\vec{e}_1\hspace{0.5em} \vec{e}_2])=\det(I)</m>?
</p>
<figure>
<image width="75%" xml:id="GT1-image-identity-determinant">
<image width="50%" xml:id="GT1-image-identity-determinant">
<latex-image>
\begin{tikzpicture}
\fill[red!50!white] (0,0) rectangle (1,1);
Expand Down
2 changes: 1 addition & 1 deletion source/linear-algebra/source/05-GT/03.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -15,7 +15,7 @@
<activity>
<introduction>
<p>
Let <m>R\colon\IR^2\to\IR^2</m> be the transformation given by rotating vectors about the origin through and angle of <m>45^\circ</m>, and let <m>S\colon\IR^2\to\IR^2</m> denote the transformation that reflects vectors about the line <m>x_1=x_2</m>.
Let <m>R\colon\IR^2\to\IR^2</m> be the transformation given by rotating vectors about the origin through an angle of <m>45^\circ</m>, and let <m>S\colon\IR^2\to\IR^2</m> denote the transformation that reflects vectors about the line <m>x_1=x_2</m>.
</p>
</introduction>
<task>
Expand Down
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