Answer
See solution
Work Step by Step
Get the Solve of equation $\mathbf{x}=C \mathbf{x}+\mathbf{d}:$
\[
\begin{array}{l}
\mathrm{d}=\mathrm{x}-C \mathrm{x}=\left[\begin{array}{c}
x_{1} \\
x_{2} \\
x_{3}
\end{array}\right]-\left[\begin{array}{ccc}
0.10 & 0.60 & 0.60 \\
0.30 & 0.20 & 0.00 \\
0.30 & 0.10 & 0.10
\end{array}\right]\left[\begin{array}{c}
x_{1} \\
x_{2} \\
x_{3}
\end{array}\right] \\
\mathrm{d}=\left[\begin{array}{ccc}
0.9 x_{1} & -0.6 x_{2} & -0.6 x_{3} \\
-0.3 x_{1} & 0.8 x_{2} & 0 \\
-0.3 x_{1} & -0.1 x_{2} & 0.9 x_{3}
\end{array}\right]=\left[\begin{array}{c}
0 \\
18 \\
0
\end{array}\right]
\end{array}
\]
This system of equations has the augmented matrix
\[
\left[\begin{array}{cccc}
0.9 & -0.6 & -0.6 & 0 \\
-0.3 & 0.8 & 0 & 18 \\
-0.3 & -0.1 & 0.9 & 0
\end{array}\right]=\left[\begin{array}{cccc}
1 & 0 & 0 & 33.33 \\
0 & 1 & 0 & 35.00 \\
0 & 0 & 1 & 15.00
\end{array}\right]
\]
So manufacturing needs to produce about 33 units, agriculture needs to produce 35 units, and services needs to produce 15 units to meet a final. demand of 18 units of agriculture.
