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Fix output directory
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siwelwerd committed Nov 17, 2020
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Expand Down Expand Up @@ -256,10 +256,10 @@ <h1 class="heading"><a href="linear-algebra-for-team-based-inquiry-learning.html
\left[\begin{array}{c} 2 \\ 3\end{array}\right]
\right)
=
\left[\begin{array}{c} 1 \\ 0 \\ 4 \\ -1 \end{array}\right] +
\left[\begin{array}{c} 5 \\ 4 \\ 6 \\ -5 \end{array}\right]
\left[\begin{array}{c} 1 \\ 0 \\ 4 \\ 0 \end{array}\right] +
\left[\begin{array}{c} 5 \\ 4 \\ 6 \\ -1 \end{array}\right]
=
\left[\begin{array}{c} 6 \\ 4 \\ 10 \\ -6 \end{array}\right]
\left[\begin{array}{c} 6 \\ 4 \\ 10 \\ -1 \end{array}\right]
\end{equation*}
</div>
<p id="p-460">Since the resulting vectors are different, \(T\) is not a linear transformation.</p></article></div>
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Expand Down Expand Up @@ -209,7 +209,7 @@ <h1 class="heading"><a href="linear-algebra-for-team-based-inquiry-learning.html
<p id="p-545">Let \(T: \IR^3 \rightarrow \IR^2\) be the linear transformation given by the standard matrix</p>
<div class="displaymath">
\begin{equation*}
T\left( \left[\begin{array}{c} x \\ y \\ z \end{array}\right] = \left[\begin{array}{c} 3x+4y-z \\ x+2y+z \end{array}\right]\right)
T\left( \left[\begin{array}{c} x \\ y \\ z \end{array}\right]\right) = \left[\begin{array}{c} 3x+4y-z \\ x+2y+z \end{array}\right]
\end{equation*}
</div>
</div>
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Expand Down Expand Up @@ -422,7 +422,8 @@ <h1 class="heading"><a href="linear-algebra-for-team-based-inquiry-learning.html
\end{array}\right]
\end{equation*}
</div></article></div>
<section class="exercises" id="exercises-1"><h3 class="heading hide-type">
<figure class="figure figure-like" id="figure-1"><div class="video-box" style="width: 100%;padding-top: 56.25%; margin-left: 0%; margin-right: 0%;"><video id="video-E1" class="video" controls=""><source src="https://southalabama.hosted.panopto.com/Panopto/Podcast/StreamInBrowser/266e0be9-9533-4df2-8a1c-ac1a0142a06a.mp4?mediaTargetType=videoPodcast" type="video/mp4"></source>Your browser does not support the &lt;video&gt; tag.<track label="US English" kind="subtitles" srclang="en" src="videos/E1-captions.vtt"></track></video></div>
<figcaption><span class="type">Figure</span><span class="space"> </span><span class="codenumber">1.1.12<span class="period">.</span></span><span class="space"> </span>Video example: Converting between systems, vector equations, and augmented matrices</figcaption></figure><section class="exercises" id="exercises-1"><h3 class="heading hide-type">
<span class="type">Exercises</span> <span class="codenumber">1.1.1</span> <span class="title">Exercises</span>
</h3>
<article class="exercise exercise-like" id="exercise-1"><h6 class="heading"><span class="codenumber">1<span class="period">.</span></span></h6>
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Expand Down Expand Up @@ -163,7 +163,7 @@ <h1 class="heading"><a href="linear-algebra-for-team-based-inquiry-learning.html
<span class="type">Activity</span><span class="space"> </span><span class="codenumber">5.1.2</span><span class="period">.</span>
</h6>
<div class="introduction" id="introduction-38">
<p id="p-790">The image below illustrates how the linear transformation \(S : \IR^2 \rightarrow \IR^2\) given by the standard matrix \(B = \left[\begin{array}{cc} 2 &amp; 3 \\ 0 &amp; 4 \end{array}\right]\text{.}\) transforms the unit square.</p>
<p id="p-790">The image below illustrates how the linear transformation \(S : \IR^2 \rightarrow \IR^2\) given by the standard matrix \(B = \left[\begin{array}{cc} 2 &amp; 3 \\ 0 &amp; 4 \end{array}\right]\) transforms the unit square.</p>
<pre class="code-block tex2jax_ignore">
\begin{tikzpicture}[scale=0.5]
\fill[red!50!white] (0,0) rectangle (1,1);
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\begin{equation*}
A=\left[\begin{array}{cccc}1&amp;2&amp;3 &amp; 4\\5&amp;6 &amp; 7 &amp; 8\\9 &amp; 10 &amp; 11 &amp; 12 \\ 13 &amp; 14 &amp; 15 &amp; 16\end{array}\right]
\sim
\left[\begin{array}{cccc}1+4(9)&amp;2+4(10)&amp;3+4(11) &amp; 4+4(12) \\5&amp;6 &amp; 6 &amp; 8\\9 &amp; 10 &amp; 11 &amp; 12 \\ 13 &amp; 14 &amp; 15 &amp; 16\end{array}\right]=B
\left[\begin{array}{cccc}1+4(9)&amp;2+4(10)&amp;3+4(11) &amp; 4+4(12) \\5&amp;6 &amp; 7 &amp; 8\\9 &amp; 10 &amp; 11 &amp; 12 \\ 13 &amp; 14 &amp; 15 &amp; 16\end{array}\right]=B
\end{equation*}
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<ol class="lower-alpha">
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<div class="author-info">Department of Mathematics and Statistics<br>University of South Alabama<br><a href="mailto:[email protected]">[email protected]</a>
</div>
</div>
<div class="date">September 26, 2020</div></section></div></main>
<div class="date">November 17, 2020</div></section></div></main>
</div>
</body>
</html>
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