<div class="checkit exercise" data-checkit-slug="M2" data-checkit-title="Row operations as matrix multiplication" data-checkit-seed="0004">
 <div class="exercise-statement">
 Let \(A\) be a \(4 \times 4\) matrix.
 <ol type="a">
 <li>Give a \(4 \times 4\) matrix \(Q\) that may be used to perform the row operation \( R_1 \to R_1 + 2R_2 \).</li>
 <li>Give a \(4 \times 4\) matrix \(C\) that may be used to perform the row operation \( R_3 \leftrightarrow R_2 \).</li>
 <li>Use matrix multiplication to describe the matrix obtained by applying \( R_3 \leftrightarrow R_2 \) and then \( R_1 \to R_1 + 2R_2 \) to \(A\) (note the order). </li>
 </ol>
 </div>
 <div class="exercise-answer">
 
 Answer:
 
 <ol type="a">
 <li>
 \(Q= \left[\begin{array}{cccc}
1 &amp; 2 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{array}\right] \)
 </li>
 <li>
 \(C= \left[\begin{array}{cccc}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{array}\right] \)
 </li>
 <li>
 \(QCA\)
 </li>
 </ol>
 </div>
</div>

Collaborative Calculation and Data Science

colby

sagemath

Product

Resources

Company