Chapter 4.7, Problem 12E

Problems $9\text{-}14$ pertain to the following input-output model: Assume that an economy is based on two industrial sectors, agriculture $\left(A\right)$ and energy $\left(E\right)$. The technology matrix $M$ and final demand matrices (in billions of dollars) are

$\begin{array}{l}\begin{array}{ccc}& A& E\end{array}\\ \begin{array}{c}A\\ E\end{array}\left[\begin{array}{cc}0.4& 0.2\\ 0.2& 0.1\end{array}\right]=M\end{array}$

$D_1=\left[\begin{array}{c}6\\ 4\end{array}\right]D_2=\left[\begin{array}{c}8\\ 5\end{array}\right]D_3=\left[\begin{array}{c}12\\ 9\end{array}\right]$

Find the output for each sector that is needed to satisfy the final demand $D_1$.