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

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

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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.

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