#### Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 5 sub question (ii)

82

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: $\begin{bmatrix} 1 &2 &3 \end{bmatrix} \begin{bmatrix} 1 &0 &2 \\ 2& 0& 1\\ 0& 1 &2 \end{bmatrix}\begin{bmatrix} 2\\ \4\\ 6 \end{bmatrix}$

Firstly, we have to multiply first two given matrices,

$\begin{bmatrix} 1 &2 &3 \end{bmatrix} \begin{bmatrix} 1 &0 &2 \\ 2& 0& 1\\ 0& 1 &2 \end{bmatrix}$

$=\begin{bmatrix} 1 \times 1 + 2 \times 2+ 3 \times 0 & 1 \times 0 + 2 \times 0 + 3 \times 1 &1 \times 2 +2 \times + 3 \times 2 \end{bmatrix}$

$=\begin{bmatrix} 1+4 +0 & 0+0+3 &2 + 2+6 \end{bmatrix}$

$=\begin{bmatrix} 5 & 3 &10 \end{bmatrix}$

Now we multiply the above row matrix with third matrix

$\begin{bmatrix} 5 & 3 &10 \end{bmatrix}\begin{bmatrix} 2\\ 4\\ 6 \end{bmatrix}$

$[5\times 2 +3 \times 4 +10 \times 6]=[10+12+60]=82$