Chapter 10, Problem 7P

Perform Crout decomposition on

$\begin{array}{c}2x_1-5x_2+x_3=12\\ -x_1+3x_2-x_3=-8\\ 3x_1-4x_2+2x_3=16\end{array}$

Then, multiply the resulting $\left[L\right]$ and $\left[U\right]$ matrices to determine that $\left[A\right]$ is produced.