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Explain solution for rd sharma class class 12 chapter Algebra of matrices exercise 4.3 question 48 sub question (iv) math

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Answer: A = [ -4]

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} 2 & 1 & 3 \end{array}\right]\left[\begin{array}{ccc} -1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right]=A \\\\\\ \Rightarrow A=\left[\begin{array}{lll} 2 & 1 & 3 \end{array}\right]\left[\begin{array}{ccc} -1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right] \\\\\\ \Rightarrow A=[2(-1)+(1)(-1)+3(0) \quad 2(0)+1(1)+3(1) \quad 2(-1)+1(0)+3(1)]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right] \\

\\\\ \Rightarrow A=\left[\begin{array}{lll} -2-1+0 & 0+1+3 \quad-2+0+3 \end{array}\right]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right] \\\\\\ \Rightarrow A=\left[\begin{array}{ccc} -3 & 4 & 1 \end{array}\right]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right] \\\\\\ \Rightarrow A=[(-3)(1)+4(0)+1(-1)]\\\\\Rightarrow A=[-3+0-1] \\\\ \Rightarrow A=[-4]

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