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publication/publication-619.ptx

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<geometry>papersize={7in,10in},margin=1in</geometry>
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</page>
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<asymptote links="no" />
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<insertions pagebreaks="LE1-individual-practice LE2-activity-identify-row-ops LE2-activity-complete-RREF"/>
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<insertions pagebreaks="EV1-activity-sketch3 EV3-activity-arbitrary EV3-p-two-chains EV6-observation-dimension"/>
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<insertions pagebreaks="AT2-exercises AT3-activity-basis-kernel AT4-activity-not-surjective-dim"/>
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<insertions pagebreaks="GT1-individual-practice GT4-individual-practice"/>
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</latex>
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source/linear-algebra/source/01-LE/01.ptx

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</activity>
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</subsection>
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<subsection>
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<subsection xml:id="LE1-individual-practice">
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<title>Individual Practice</title>
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<activity>
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<introduction>

source/linear-algebra/source/01-LE/02.ptx

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</activity>
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<activity estimated-time='5'>
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<activity estimated-time='5' xml:id="LE2-activity-identify-row-ops">
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<statement>
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<p>
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Here we've written the sorted linear systems from <xref ref="LE2-activity-sort"/>
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</p>
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</observation>
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<activity estimated-time='10'>
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<activity estimated-time='10' xml:id="LE2-activity-complete-RREF">
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<statement>
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<p>
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Complete the following RREF calculation (multiple row operations may be needed

source/linear-algebra/source/02-EV/01.ptx

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</statement>
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</definition>
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<activity estimated-time='10'>
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<activity estimated-time='10' xml:id="EV1-activity-sketch">
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<introduction>
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<p>
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Consider <m>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right]\right\}</m>.
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<activity estimated-time='10'>
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<activity estimated-time='10' xml:id="EV1-activity-sketch2">
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<introduction>
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<p>
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Consider <m>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right],
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</task>
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</activity>
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<activity estimated-time='5'>
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<activity estimated-time='5' xml:id="EV1-activity-sketch3">
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<statement>
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<p component="html">
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Sketch a representation of all the vectors belonging to

source/linear-algebra/source/02-EV/03.ptx

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</statement>
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</definition>
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<activity estimated-time='5' xml:id="EV3-activity-arbitrary">
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<introduction>
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<p>
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Consider an arbitrary homogeneous vector equation <m>x_1 \vec{v}_1 + \cdots+x_n \vec{v}_n = \vec{0}</m>.
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<li>
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<p>
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Using two chains of equalities:
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</p>
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<p xml:id="EV3-p-two-chains">
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<md>
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<mrow>
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\mathrm{LEFT} &amp;= \cdots &amp; \mathrm{RIGHT} &amp;=\cdots

source/linear-algebra/source/02-EV/06.ptx

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<sage language="octave" component="html">
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</sage>
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<observation>
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<observation xml:id="EV6-observation-dimension">
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<p>
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Even though we found different bases for them,
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<m>\vspan S</m> and <m>\vspan T</m> are exactly the same subspace of <m>\IR^4</m>,

source/linear-algebra/source/03-AT/02.ptx

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<subsection>
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<subsection xml:id="AT2-exercises">
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<title>Exercises</title>
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<p component="preview">
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Exercises available at <url href="https://tbil.org/preview/linear-algebra/exercises/#/bank/AT2/"/>

source/linear-algebra/source/03-AT/03.ptx

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</statement>
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</observation>
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<activity estimated-time='10' xml:id="AT3-activity-basis-kernel">
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<statement>
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<p>
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Let <m>T: \IR^4 \rightarrow \IR^3</m> be the linear transformation whose standard matrix is:

source/linear-algebra/source/03-AT/04.ptx

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</p>
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</observation>
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<activity estimated-time='3'>
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<activity estimated-time='3' xml:id="AT4-activity-not-surjective-dim">
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<statement>
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<p>
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What can you conclude about the linear map

source/linear-algebra/source/05-GT/01.ptx

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transforms the unit square.
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</p>
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<figure xml:id="GT1-unit-square-transform">
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<image width="75%" xml:id="GT1-image-unit-square-transform">
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<image width="65%" xml:id="GT1-image-unit-square-transform">
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<latex-image>
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\begin{tikzpicture}
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\fill[red!50!white] (0,0) rectangle (1,1);
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</observation>
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</subsection>
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<subsection>
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<subsection xml:id="GT1-individual-practice">
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<title>Individual Practice</title>
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<activity>
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<introduction>

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