Chapter 1.5, Problem 8E

Compute the LU factorization of each of the following matrices.

(a) $\left[\begin{array}{cc}\begin{array}{l}3\\ 9\end{array}& \begin{array}{l}1\\ 5\end{array}\end{array}\right]$

(b) $\left[\begin{array}{cc}\begin{array}{l}2\\ -2\end{array}& \begin{array}{l}4\\ 1\end{array}\end{array}\right]$

(c) $\left[\begin{array}{ccc}\begin{array}{l}1\\ 3\\ -2\end{array}& \begin{array}{l}1\\ 5\\ 2\end{array}& \begin{array}{l}1\\ 6\\ 7\end{array}\end{array}\right]$

(d) $\left[\begin{array}{ccc}\begin{array}{l}-2\\ 4\\ -6\end{array}& \begin{array}{l}1\\ 1\\ -3\end{array}& \begin{array}{l}2\\ -2\\ 4\end{array}\end{array}\right]$