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  • Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question (71) math

Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question (71) math

Answers (1)

Answer: Bill of A=Rs 157.80, bill of B=Rs 167.40 and bill of C=Rs 281.40

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: Three shopkeepers A, B and C.

 A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils.

B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils.

C purchase 11 dozen notebooks, 13 dozen pens and 8 dozen pencils.

Cost of notebook=40 paise = Rs 0.40

Cost of pen=Rs 1.25

Cost of pencil=35 paise = Rs 0.35

The number of items purchased by A, B and C are represented in matrix form as,

[As we know 1 dozen=12 quantity]

                                       \text { Notebooks } \begin{array}{l} \text { Pens } \end{array} \text { Pencils }\\

               \begin {aligned} & \begin{array}{l} X=\begin{array}{c} A \\ B \\ C \end{array}\left[\begin{array}{ccc} 12 \times 12 & 5 \times 12 & 6 \times 12 \\ 10 \times 12 & 6 \times 12 & 7 \times 12 \\ 11 \times 12 & 13 \times 12 & 8 \times 12 \end{array}\right] \end{array} \end {aligned}

                X=\begin{array}{c} A \\ B \\ C \end{array}\left[\begin{array}{ccc} 144 & 60 & 72 \\ 120 & 72 & 84 \\ 132 & 156 & 96 \end{array}\right]

Now, matrix formed by the cost of each item is given by,

                 Y = \left[\begin{array}{l} 0.40 \\ 1.25 \\ 0.35 \end{array}\right]

Individual bill can be calculated by           

              \\X Y=\left[\begin{array}{lll} 144 & 60 & 72 \\ 120 & 72 & 84 \\ 132 & 156 & 96 \end{array}\right]\left[\begin{array}{l} 0.40 \\ 1.25 \\ 0.35 \end{array}\right] \\\\ X Y=\left[\begin{array}{l} 157.80 \\ 167.40 \\ 281.40 \end{array}\right]

So,

Bill of A=Rs 157.80

Bill of B=Rs 167.40

Bill of C=Rs 281.40

Posted by

infoexpert22

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