Answer
$\left[\begin{array}{l}110 \\ 120\end{array}\right]$
Work Step by Step
\[
\begin{array}{l}
x=C x+d \\
=(I-C) x+d \\
x=(I-C)^{-1} d
\end{array}
\]
Given production model.
\[
I-C=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]-\left[\begin{array}{cc}
0 & .5 \\
.6 & .2
\end{array}\right]=\left[\begin{array}{cc}
1 & -.5 \\
-.6 & .8
\end{array}\right]
\]
Find the value of I-C.
\[
(I-C)^{-1}=\left[\begin{array}{ll}
1.6 & 1 \\
1.2 & 2
\end{array}\right]
\]
Inverse of I-C.
\[
x=\left[\begin{array}{ll}
1.6 & 1 \\
1.2 & 2
\end{array}\right]\left[\begin{array}{l}
50 \\
30
\end{array}\right]=\left[\begin{array}{l}
110 \\
120
\end{array}\right]
\]
