Chapter 4, Problem 36RE

Given the technology matrix $M$ and the final demand matrix $D$ (in billions of dollars), find ${\left(I-M\right)}^{-1}$ and the output matrix $X$ :

$M=\left[\begin{array}{ccc}0.2& 0& 0.4\\ 0.1& 0.3& 0.1\\ 0& 0.4& 0.2\end{array}\right]D=\left[\begin{array}{c}40\\ 20\\ 30\end{array}\right]$