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  • Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question 19

Provide solution for rd sharma math class class 12 chapter Algebra of matrices exercise 4.3 question 19

Answers (1)

Answer: a_{43} = 8 \ \ and \ \ a _{ 22} =0

Hint:

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

 a_{43} means element from 4th row and 3rd column and \ \ a _{ 22} =0 means element from 2nd row and 2nd column.

 

Given:

\left[\begin{array}{ccc}0 & 1 & 0 \\ 2 & 0 & 2 \\ 0 & 3 & 2 \\ 4 & 0 & 4\end{array}\right]\left[\begin{array}{cc}2 & -1 \\ -3 & 2 \\ 4 & 3\end{array}\right]\left[\begin{array}{ccccc}0 & 1 & -1 & 2 & -2 \\ 3 & -3 & 4 & -4 & 0\end{array}\right]

Firstly, we will multiply first two matrices

Then,

A=\left[\begin{array}{cc}0-3+0 & 0+2+0 \\ 4+0+8 & -2+0+6 \\ 0-9+8 & 0+6+6 \\ 8+0+16 & -4+0+12\end{array}\right]\left[\begin{array}{ccccc}0 & 1 & -1 & 2 & -2 \\ 3 & -3 & 4 & -4 & 0\end{array}\right] \\\\\\ A=\left[\begin{array}{cc}-3 & 2 \\ 12 & 4 \\ -1 & 12 \\ 24 & 8\end{array}\right]\left[\begin{array}{ccccc}0 & 1 & -1 & 2 & -2 \\ 3 & -3 & 4 & -4 & 0\end{array}\right] \\\\\\ A=\left[\begin{array}{ccccc}0+6 & -3-6 & 3+8 & -6-8 & 6+0 \\ 0+12 & 12-12 & -12+16 & 24-16 & -24+0 \\ 0+36 & -1-36 & 1+48 & -2-48 & 2+0 \\ 0+24 & 24-24 & -24+32 & 48-32 & -48+0\end{array}\right] \\\\ \\ A=\left[\begin{array}{ccccc}6 & -9 & 11 & -14 & 6 \\ 12 & 0 & 4 & 8 & -24 \\ 36 & -37 & 49 & -50 & 2 \\ 24 & 0 & 8 & 16 & -48\end{array}\right]

Then,a_{43} = 8 \ \ and \ \ a _{ 22} =0

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