#### Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question 77

Answer: The total amount spent by the party in the two cities (in Rs)

$=\begin {array} {c} X \\Y \end{array} \left[\begin{array}{c}9900 \\ 21200\end{array}\right]$

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: The cost per contact(in paisa)

$A=\left[\begin{array}{c}140 \\ 200 \\ 150\end{array}\right] \begin{array}{c}\text { telephone } \\ \text { house calls } \\ \text { letters }\end{array}$

The number of contacts of each type made in two cities X and Y is

$B=\left[\begin{array}{ccc}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{array}\right] \begin{array}{c}X\\Y\end{array}$

The total amount of money spent by party in each of the cities for the election is given by the matrix:

$\\B A=\left[\begin{array}{ccc} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{array}\right]\left[\begin{array}{c} 140 \\ 200 \\ 150 \end{array}\right]\\\\\\ =\left[\begin{array}{c} 1000 \times 140+500 \times 200+5000 \times 150 \\ 3000 \times 140+1000 \times 200+10000 \times 150 \end{array}\right]\\\\\\ =\begin{array}{c} X \\ Y \end{array}\left[\begin{array}{c} 140000+100000+750000 \\ 420000+200000+1500000 \end{array}\right]\\\\\\ =\begin{array}{c} X \\ Y \end{array}\left[\begin{array}{c} 990000 \\ 2120000 \end{array}\right]$

The total amount of money spent by party in each of the cities for the election in Rs is given by

$\\=\left(\frac{1}{100}\right)_{Y}^{X}\left[\begin{array}{c} 990000 \\ 2120000 \end{array}\right]\\\\\\ =\begin{array}{c} X \\ Y \end{array}\left[\begin{array}{c} 9900 \\ 21200 \end{array}\right]$

One should consider social activities before casting his/her vote for the party.