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  • Need solution for RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 17 sub question (i) maths textbook solution

Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 17 (i) maths textbook solution

Answers (1)

Answer:

Hence, verify the distribution of matrix multiplication over matrix addition A(B+C)=A B+ A C

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:A=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right], B=\left[\begin{array}{cc}-1 & 0 \\ 2 & 1\end{array}\right], C=\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]

Consider,

A(B+C) \\\\ =\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\left(\left[\begin{array}{cc}-1 & 0 \\ 2 & 1\end{array}\right]+\left[\begin{array}{ll}0 & 1 \\ 1 & -1\end{array}\right]\right) \\\\\\ = \left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\left(\left[\begin{array}{cc}-1+0 & 0+1 \\ 2+1 & 1-1\end{array}\right]\right)=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{cc}-1 & 1 \\ 3 & 0\end{array}\right] \\\\

\begin{bmatrix} -1-3 & 1+0 \\ -0+6& 0+0 \end{bmatrix} 

A(B+C)=\left[\begin{array}{cc} -4 & 1 \\ 6 & 0 \end{array}\right]

 

A B+A C=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{cc}-1 & 0 \\ 2 & 1\end{array}\right]+\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\left[\begin{array}{cc}0 & 1 \\ 1 & -1\end{array}\right]\\\\\\=\left[\begin{array}{cc}1(-1)+(-1)(2) & 1(0)+(-1)(1) \\0(-1)+2(2) & 0(0)+2(1)\end{array}\right]+\left[\begin{array}{cc}(1)(0)+(-1)(1) & 1(1)+(-1)(-1) \\ 0(0)+2(1) & 0(1)+2(-1)\end{array}\right] \\\\\\=\left[\begin{array}{ll}-1-2 & 0-1 \\ -0+4 & 0+2\end{array}\right]+\left[\begin{array}{ll}0-1 & 1+1 \\ 0+2 & 0-2\end{array}\right]

A B+A C=\left[\begin{array}{cc} -4 & 1 \\ 6 & 0 \end{array}\right]

From equation i & equation ii

A(B+C)=A B+ A C

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