If $\begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix}$ = 0, then value of $x$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -1
Given:
$[1\ 2\ 1]\begin{bmatrix}1&2&0\\2&0&1\\1&0&2\end{bmatrix}\begin{bmatrix}0\\2\\x\end{bmatrix}$ = 0
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:
$4+4x=0 \Rightarrow x=-1$
$x=-1$