Chapter 4, Problem 29RE

An economy is based on two sectors, agriculture and energy. 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 $X$ :

$\begin{array}{l}\begin{array}{cc}A& E\end{array}\\ M=\begin{array}{c}A\\ E\end{array}\left[\begin{array}{cc}0.2& 0.15\\ 0.4& 0.3\end{array}\right]D=\begin{array}{c}A\\ E\end{array}\left[\begin{array}{c}30\\ 20\end{array}\right]\end{array}$