Find the production matrix for the input-output and demand matrices using the open model.
-$$
A=\left[\begin{array}{ll}
0.2 & 0.1 \
0.5 & 0.4
\end{array}\right], D=\left[\begin{array}{l}
3 \
6
\end{array}\right]
$$
A) $ \left[\begin{array}{r}5.13 \ 14.65\end{array}\right] $
B) $ \left[\begin{array}{r}5.58 \ 14.65\end{array}\right] $
C) $ \left[\begin{array}{l}5.55 \ 7.88\end{array}\right] $
D) $ \left[\begin{array}{r}6.98 \ 18.31\end{array}\right] $

Question

Quizplus · Accepted Answer

The production matrix $ X $ is found using the formula $ X = (I - A)^{-1}D $. First, calculate $ I - A $, then find its inverse, and multiply by $ D $. The correct result is $ \left[\begin{array}{r}5.58 \ 14.65\end{array}\right] $.

Find the Production Matrix for the Input-Output and Demand Matrices A=[0.20.10.50.4],D=[36]A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]A=[0.20.5​0.10.4​],D=[36​]

Find the Production Matrix for the Input-Output and Demand Matrices $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$