Problem 2:
Matrix inversion requires forward substitution and Back substitution after the decomposition of
coefficient matrix A into [L] and [U]. Show hand calculations of the third column of $A^{-1}$ and
verify it by MATLAB.
Given that,
$\begin{bmatrix} 1 & \frac{1}{2} & \frac{1}{3} \\ 0 & \frac{1}{6} & \frac{1}{6} \\ 0 & 0 & \frac{1}{60} \end{bmatrix} = [U]$,
$\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & \frac{3}{2} & 1 \end{bmatrix} = [L]$
Instructions:
• [C] = Third column of the identity matrix
• Solve [L][Z] = [C] for [Z]
