Chapter 10, Problem 11P

Use the following LU decomposition to (a) compute the determinant and (b) solve $\left[A\right]\left\{x\right\}=\left\{b\right\}\text{ with }{\left\{b\right\}}^T=\left[-1044-26\right]$.

$\left[A\right]=\left[L\right]\left[U\right]=\left[\begin{array}{ccc}1& & \\ 0.6667& 1& \\ -0.3333& -0.3636& 1\end{array}\right]\left[\begin{array}{ccc}3& -2& 1\\ & 7.3333& -4.6667\\ & & 3.6364\end{array}\right]$