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<h1 id="linear-algebra-review">Linear Algebra Review</h1>
<h2 id="gauss-elimination-suggested-problems">(Gauss Elimination) Suggested problems</h2>
<h3 id="no-due-date">No due date</h3>
<ol style="list-style-type: decimal">
<li><p>Determine the lower (L) and upper (U) triangular matrices with LU-decomposition for the following matrices:</p>
<ol style="list-style-type: lower-alpha">
<li><p><span class="math inline">\(A=\left[ \begin{array}{cc} 1 &amp; 3 \\ 2 &amp; 1 \end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{cc} 1 &amp; 1 \\ 2 &amp; 3 \end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{cc} 1 &amp; 1 \\ 2 &amp; -2 \end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 &amp; 3 &amp; 1 \\ -4 &amp; -9 &amp; 2 \\ 0 &amp; 3 &amp; 6\end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 &amp; 3 &amp; 1 \\ -4 &amp; -9 &amp; 2 \\ 0 &amp; 3 &amp; 6\end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 &amp; 3 &amp; -5 \\ 1 &amp; 4 &amp; -8 \\ -3 &amp; -7 &amp; 9\end{array} \right]\)</span></p></li>
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 &amp; 2 &amp; -1 \\ 2 &amp; 2 &amp; 2 \\ 1 &amp; -1 &amp; 2\end{array} \right]\)</span></p></li>
</ol></li>
<li><p>Calculate the determinant of A from 1a-g.</p></li>
<li><p>Determine the Cholesky factorization, C, of the following matrices, where</p>
<p><span class="math inline">\(C_{ii}=\sqrt{a_{ii}-\sum_{k=1}^{i-1}C_{ki}^{2}}\)</span></p>
<p><span class="math inline">\(C_{ij}=\frac{a_{ij}-\sum_{k=1}^{i-1}C_{ki}C_{kj}}{C_{ii}}\)</span>.</p>
<ol style="list-style-type: lower-alpha">
<li><p>A=<span class="math inline">\(\left[ \begin{array}{cc} 3 &amp; 2 \\ 2 &amp; 1 \end{array} \right]\)</span></p></li>
<li><p>A=<span class="math inline">\(\left[ \begin{array}{cc} 10 &amp; 5 \\ 5 &amp; 20 \end{array} \right]\)</span></p></li>
<li><p>A=<span class="math inline">\(\left[ \begin{array}{ccc} 10 &amp; -10 &amp; 20 \\ -10 &amp; 20 &amp; 10 \\ 20 &amp; 10 &amp; 30 \end{array} \right]\)</span></p></li>
<li><p>A=<span class="math inline">\(\left[ \begin{array}{cccc} 21 &amp; -1 &amp; 0 &amp; 0 \\ -1 &amp; 21 &amp; -1 &amp; 0 \\ 0 &amp; -1 &amp; 21 &amp; -1 \\ 0 &amp; 0 &amp; -1 &amp; 1 \end{array} \right]\)</span></p></li>
</ol></li>
<li><p>Verify that <span class="math inline">\(C^{T}C=A\)</span> for 3a-d</p></li>
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