<item ident="G2-0006" title="G2 | Determinants | ver. 0006"> <itemmetadata> <qtimetadata> <qtimetadatafield> <fieldlabel>question_type</fieldlabel> <fieldentry>essay_question</fieldentry> </qtimetadatafield> </qtimetadata> </itemmetadata> <presentation> <material> <mattextxml> <div class="exercise-statement"> <p> <strong>G2.</strong> </p> <p>Show how to compute the determinant of the matrix <p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A= \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] ." alt="A= \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] ." title="A= \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] ." data-latex="A= \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] ."/></p>.</p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-statement"> <p> <strong>G2.</strong> </p> <p>Show how to compute the determinant of the matrix </p> <p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?A=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%203%20&amp;%200%20&amp;%204%20&amp;%20-1%20%5C%5C%20-2%20&amp;%20-1%20&amp;%200%20&amp;%200%20%5C%5C%20-3%20&amp;%20-5%20&amp;%202%20&amp;%206%20%5C%5C%206%20&amp;%202%20&amp;%201%20&amp;%203%20%5Cend%7Barray%7D%5Cright%5D%20." alt="A= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] ." title="A= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] ." data-latex="A= \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] ."></p>. </div> </mattext> </material> <response_str ident="response1" rcardinality="Single"> <render_fib> <response_label ident="answer1" rshuffle="No"/> </render_fib> </response_str> </presentation> <itemfeedback ident="general_fb"> <flow_mat> <material> <mattextxml> <div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] = 39" alt="\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] = 39" title="\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] = 39" data-latex="\operatorname{det}\ \left[\begin{array}{cccc} 3 & 0 & 4 & -1 \\ -2 & -1 & 0 & 0 \\ -3 & -5 & 2 & 6 \\ 6 & 2 & 1 & 3 \end{array}\right] = 39"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Coperatorname%7Bdet%7D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D%203%20&amp;%200%20&amp;%204%20&amp;%20-1%20%5C%5C%20-2%20&amp;%20-1%20&amp;%200%20&amp;%200%20%5C%5C%20-3%20&amp;%20-5%20&amp;%202%20&amp;%206%20%5C%5C%206%20&amp;%202%20&amp;%201%20&amp;%203%20%5Cend%7Barray%7D%5Cright%5D%20=%2039" alt="\operatorname{det}\ \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] = 39" title="\operatorname{det}\ \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] = 39" data-latex="\operatorname{det}\ \left[\begin{array}{cccc} 3 &amp; 0 &amp; 4 &amp; -1 \\ -2 &amp; -1 &amp; 0 &amp; 0 \\ -3 &amp; -5 &amp; 2 &amp; 6 \\ 6 &amp; 2 &amp; 1 &amp; 3 \end{array}\right] = 39"> </p> </div> </mattext> </material> </flow_mat> </itemfeedback> </item>