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  • Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 40 sub question (ii) math

Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 40 sub question (ii) math

Answers (1)

Answer:  x=-1 

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

First we multiply first two matrices,\begin {array}{ll}\Rightarrow[1(1)+2(2)+(1)(1) \quad 1(2)+2(0)+1(0) \quad 1(0)+2(1)+1(2)]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0\\\\ \Rightarrow\left[\begin{array}{lll}1+4+1 & 2+0+0 & 0+2+2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0 \end{}

\begin {array}{ll}\\\\\Rightarrow\left[\begin{array}{lll}6 & 2 & 4\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0\\\\ \Rightarrow[0+2(2)+4(x)]=0\\\\ \Rightarrow 4+4 x=0\\\\ \Rightarrow 4 x=-4 \end{}

\begin {array}{ll}\\\\\Rightarrow x = -\frac{4}{4} = -1 \end{}

Therefore, x=-1

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