Permalink
Cannot retrieve contributors at this time
Name already in use
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
ME3255S2017/linear_algebra/LU_suggested.html
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
39 lines (39 sloc)
3.06 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> | |
<html xmlns="http://www.w3.org/1999/xhtml"> | |
<head> | |
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> | |
<meta http-equiv="Content-Style-Type" content="text/css" /> | |
<meta name="generator" content="pandoc" /> | |
<title></title> | |
<style type="text/css">code{white-space: pre;}</style> | |
<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script> | |
</head> | |
<body> | |
<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">\(A=\left[ \begin{array}{cc} 1 & 3 \\ 2 & 1 \end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{cc} 1 & 1 \\ 2 & 3 \end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{cc} 1 & 1 \\ 2 & -2 \end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 & 3 & 1 \\ -4 & -9 & 2 \\ 0 & 3 & 6\end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 & 3 & 1 \\ -4 & -9 & 2 \\ 0 & 3 & 6\end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 & 3 & -5 \\ 1 & 4 & -8 \\ -3 & -7 & 9\end{array} \right]\)</span></p></li> | |
<li><p><span class="math inline">\(A=\left[ \begin{array}{ccc} 1 & 2 & -1 \\ 2 & 2 & 2 \\ 1 & -1 & 2\end{array} \right]\)</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">\(\left[ \begin{array}{cc} 3 & 2 \\ 2 & 1 \end{array} \right]\)</span></p></li> | |
<li><p>A=<span class="math inline">\(\left[ \begin{array}{cc} 10 & 5 \\ 5 & 20 \end{array} \right]\)</span></p></li> | |
<li><p>A=<span class="math inline">\(\left[ \begin{array}{ccc} 10 & -10 & 20 \\ -10 & 20 & 10 \\ 20 & 10 & 30 \end{array} \right]\)</span></p></li> | |
<li><p>A=<span class="math inline">\(\left[ \begin{array}{cccc} 21 & -1 & 0 & 0 \\ -1 & 21 & -1 & 0 \\ 0 & -1 & 21 & -1 \\ 0 & 0 & -1 & 1 \end{array} \right]\)</span></p></li> | |
</ol></li> | |
<li><p>Verify that <span class="math inline">\(C^{T}C=A\)</span> for 3a-d</p></li> | |
</ol> | |
</body> | |
</html> |