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  • Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question 26

Provide solution for rd sharma math class class 12 chapter Algebra of matrices exercise 4.3 question 26

Answers (1)

Answer: x=2

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: \left[\begin{array}{lll}1 & -1 & x\end{array}\right]\left[\begin{array}{ccc}0 & 1 & -1 \\ 2 & 1 & 3 \\ 1 & 1 & 1\end{array}\right]\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]=0

Firstly, we multiply first two matrices

\Rightarrow\left[\begin{array}{lll}0-2+x & 1-1+x & -1-3+x\end{array}\right]\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]=0 \\\\ \Rightarrow\left[\begin{array}{lll}x-2 & x & x-4\end{array}\right]\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]=0\\\\ \Rightarrow[0(x-2)+x(1)+(x-4)(1)]=0 \\\\ \Rightarrow 0+x+x-4=0\\\\ \Rightarrow 2 x-4=0\\\\ \Rightarrow 2 x=4\\\\ \Rightarrow x=\frac{4}{2}=2

Hence, x=2

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