Chapter 10, Problem 6P

Use LU decomposition to determine the matrix inverse for the following system. Do not use a pivoting strategy, and check your results by verifying that $\left[A\right]{\left[A\right]}^{-1}=\left[l\right]$.

$\begin{array}{c}10x_1+2x_2-x_3=27\\ -3x_1-6x_2+2x_3=-61.5\\ x_1+x_2+5x_3=-21.5\end{array}$