Explain solution for rd sharma class 12 chapter Algebra of matrices exercise 4.3 question (72) math

Answer: The total amount the store will receive from selling all the items Rs 1597.20

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: 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Selling price of physics books=Rs 8.30 chemistry books=Rs 3.45 and mathematics=Rs 4.50

Matrix representation of stock of various types of book in the store is given by,

$\begin{array}{l} X=\left[\begin{array}{lll} 10 \times 12 & 8 \times 12 & 5 \times 12 \end{array}\right] \\\\ X=\left[\begin{array}{lll} 120 & 96 & 60 \end{array}\right] \end{array}$

Matrix representation of selling price of each book is given

$Y=\left[\begin{array}{l} 8.30 \\ 3.45 \\ 4.50 \end{array}\right]$

So, total amount received by the store from selling all the items is given by

$\\X Y=\left[\begin{array}{lll} 120 & 96 & 60 \end{array}\right]\left[\begin{array}{l} 8.30 \\ 3.45 \\ 4.50 \end{array}\right] \\\\ X Y=[(120)(8.30)+(96)(3.45)+(60)(4.50)] \\\\ X Y=[996+331.20+270] \\\\ X Y=[1597.20] \\\\$