Question:
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
Solution:
Number of different types of posts in any college is given by
$x=\left[\begin{array}{c}15 \\ 6 \\ 1 \\ 1\end{array}\right]$
Total number of posts of each kind in all the colleges = 30X
$=30\left[\begin{array}{c}15 \\ 6 \\ 1 \\ 1\end{array}\right]$
$=\left[\begin{array}{c}450 \\ 180 \\ 30 \\ 30\end{array}\right]$