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

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

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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] \\\\

Total received amount=Rs 1597.20

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