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  4. If [1 x 1][1 2 3 0 5 1 0 3 2][x 1 -2]=0, then the value of x is

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Q. If $\begin{bmatrix}1 & x & 1\end{bmatrix}\begin{bmatrix}1 & 2 & 3 \\ 0 & 5 & 1 \\ 0 & 3 & 2\end{bmatrix}\begin{bmatrix}x \\ 1 \\ -2\end{bmatrix}=0$, then the value of $x$ is

Matrices

Solution:

Given, $\begin{bmatrix}1 & x & 1\end{bmatrix}\begin{bmatrix}1 & 2 & 3 \\ 0 & 5 & 1 \\ 0 & 3 & 2\end{bmatrix}\begin{bmatrix}x \\ 1 \\ -2\end{bmatrix}=0$
$\Rightarrow [1 \times 1]\begin{bmatrix}x+2-6 \\ 0+5-2 \\ 0+3-4\end{bmatrix}=0$
$\Rightarrow [1 \times 1]\begin{bmatrix}{r}x-4 \\ 3 \\ -1\end{bmatrix}=0$
$\Rightarrow x-4+3 x-1=0$
$\Rightarrow x=\frac{5}{4}$