Answer
See explanation
Work Step by Step
Solve the equation $\mathbf{x}=C \mathbf{x}+\mathbf{d}:$
\[
\begin{array}{c}
\mathrm{d}=\mathrm{x}-C \mathrm{x}=\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}\right]-\left[\begin{array}{ccc}
.10 & .60 & .60 \\
.30 & .20 & .00 \\
.30 & .10 & .10
\end{array}\right]\left[\begin{array}{c}
x_{1} \\
x_{2} \\
x_{3}
\end{array}\right] \\
\mathrm{d}=\left[\begin{array}{ccc}
.9 x_{1} & -.6 x_{2} & -.6 x_{3} \\
-.3 x_{1} & .8 x_{2} & 0 \\
-.3 x_{1} & -.1 x_{2} & .9 x_{3}
\end{array}\right]=\left[\begin{array}{c}
18 \\
0 \\
0
\end{array}\right]
\end{array}
\]
This system of equations has the augmented matrix
\[
\left[\begin{array}{cccc}
.9 & -.6 & .6 & 18 \\
-.3 & .8 & 0 & 0 \\
-.3 & -.1 & .9 & 0
\end{array}\right]=\left[\begin{array}{cccc}
1 & 0 & 0 & 40 \\
0 & 1 & 0 & 15 \\
0 & 0 & 1 & 15
\end{array}\right]
\]
\[
\text { so } \mathbf{x}=(40,15,15)
\]\sqrt x
