Answer
$\left[\begin{array}{l}60 \\ 20 \\ 10\end{array}\right]$
Work Step by Step
First column: unit consumption vector for manutacturing
Second column: column: unit consumption vector for agriculture
Third column: unit consumption vector for services
Consumption matrix:
\[
\left[\begin{array}{ccc}
.10 & .60 & .60 \\
.30 & .20 & 0 \\
.30 & .10 & .10
\end{array}\right]
\]
Intermediate demands are calculated by $C x$ for given vector $x$.
\[
C x=\left[\begin{array}{ccc}
.10 & .60 & .60 \\
.30 & .20 & 0 \\
.30 & .10 & .10
\end{array}\right] \cdot\left[\begin{array}{c}
0 \\
100 \\
0
\end{array}\right]=\left[\begin{array}{c}
60 \\
20 \\
10
\end{array}\right]
\]
