#### Please solve RD Sharma class 12 Chapter Algebra of Matrices  exercise 4.3 question 1 sub question (iii) maths textbook solution.

$\begin{bmatrix} 14 &0 &42 \\ 18 & -1 & 56\\ 22& -2 &70 \end{bmatrix}$

Hint: matrix multiplication is only possible, when number of columns of first matrix is equal to the number of rows of second matrix.

Given: $\left[\begin{array}{lll} 2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6 \end{array}\right]\left[\begin{array}{ccc} 1 & -3 & 5 \\ 0 & 2 & 4 \\ 3 & 0 & 5 \end{array}\right]$

$=\left[\begin{array}{lll} 2 \times 1+3 \times 0+4 \times 3 & 2 \times(-3)+3 \times 2+4 \times 0 & 2 \times 5+3 \times 4+4 \times 5 \\ 3 \times 1+4 \times 0+5 \times 3 & 3 \times(-3)+4 \times 2+5 \times 0 & 3 \times 5+4 \times 4+5 \times 5 \\ 4 \times 1+5 \times 0+6 \times 3 & 4 \times(-3)+5 \times 2+6 \times 0 & 4 \times 5+5 \times 4+6 \times 5 \end{array}\right]$

$=\left[\begin{array}{ccc} 2+0+12 & -6+6+0 & 10+12+20 \\ 3+0+15 & -9+8+0 & 15+16+25 \\ 4+0+18 & -12+10+0 & 20+20+30 \end{array}\right]$

On simplification we get,

$=\begin{bmatrix} 14 &0 &42 \\ 18 & -1 & 56\\ 22& -2 &70 \end{bmatrix}$