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Q3) Attempt all three of the following.
(15 marks)
(i) Given the following technology matrix M and final demand vector d for ( 5 marks) industries \( \mathrm{A}, \mathrm{B} \) and C .
\[
M=\left[\begin{array}{lll}
0.1 & 0.3 & 0.4 \\
0.3 & 0.1 & 0.2 \\
0.2 & 0.1 & 0.3
\end{array}\right] \text { and } d=\left[\begin{array}{c}
4 \\
12 \\
16
\end{array}\right]
\]
Determine the output level required to meet the final demand for industries \( \mathrm{A}, \mathrm{B} \) and C using matrix algebra.
(ii) In an examination the number of candidates who secured marks between ( 5 marks) certain intervals were as follows
\begin{tabular}{|c|c|c|c|c|c|}
\hline Marks & \( 0-19 \) & \( 20-39 \) & \( 40-59 \) & \( 60-79 \) & \( 80-99 \) \\
\hline \begin{tabular}{c}
No. of \\
candidates
\end{tabular} & 41 & 62 & 65 & 50 & 17 \\
\hline
\end{tabular}