If $\begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix}$, then value of $x$ is

-1

The correct answer is Option (1) → -1

Given:

$[1\ 2\ 1]\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix}$

First multiply the last two matrices:

$\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix} =\begin{bmatrix}1(0)+2(2)+0(x)\\2(0)+0(2)+1(x)\\1(0)+0(2)+2(x)\end{bmatrix} =\begin{bmatrix}4\\x\\2x\end{bmatrix}$

Now multiply $[1\ 2\ 1]$ with $\begin{bmatrix}4\\x\\2x\end{bmatrix}$:

$1(4)+2(x)+1(2x)=4+4x$

From given condition, this equals 0:

$4+4x=0 \Rightarrow x=-1$

$x=-1$