If 1&-1&x 0&1&-1 2&1&3 1&1&1 0 1 1 =0, find x. - Vidyadip

Question

If $\begin{bmatrix}1&-1&\text{x}\end{bmatrix}\begin{bmatrix}0&1&-1\\2&1&3\\1&1&1\end{bmatrix}\begin{bmatrix}0\\1\\1\end{bmatrix}=0,$ find x.

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Answer

Given,
$\begin{bmatrix}1&-1&\text{x}\end{bmatrix}\begin{bmatrix}0&1&-1\\2&1&3\\1&1&1\end{bmatrix}\begin{bmatrix}0\\1\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}0-2+\text{x}&1-1+\text{x}&-1-3+\text{x}\end{bmatrix}\begin{bmatrix}0\\1\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}-2+\text{x}&\text{x}&-4+\text{x}\end{bmatrix}\begin{bmatrix}0\\1\\1\end{bmatrix}=0$
$\Rightarrow\begin{bmatrix}0+\text{x}-4+\text{x}\end{bmatrix}=0$
$ \Rightarrow2\text{x}-4=0$
$\Rightarrow2\text{x}=4$
$\Rightarrow\text{x}=\frac{4}{2}$
$\therefore\ \text{x}=2$

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