#### Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question sub question (i)

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:

$\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & -3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0$

First, we multiply first two matrices

$\begin {array}{ll}\Rightarrow\left[\begin{array}{ll}x-2 & 0-3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0 \\\ \Rightarrow\left[\begin{array}{ll}x-2 & -3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0\\\\ \Rightarrow[(x-2) x+5(-3)]=0 \\\\ \end{}$

$x^2 - 2x -15 = 0$ then solve quadratic equation

$\begin {array}{ll} \Rightarrow x^{2}-5 x+3 x-15=0 \\\\ \Rightarrow x(x-5)+3(x-5)=0\\ \\ \Rightarrow(x-5)(x+3)=0 \end {}$

$\begin {array}{ll} \Rightarrow Either \ \ x-5=0 \ \ or \ \ x+3=0 \\\\ \Rightarrow \quad x=5 \quad or \quad x=-3 \\\\So, x=5 \ \ or \ \ -3 \end {}$