If \( \begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}-1&0&1\\1&2&-1\\0&1&3\end{bmatrix}\begin{bmatrix}2x\\x\\-7\end{bmatrix}=[0] \), then the value of \( x \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Multiplying the first two matrices,
\( \displaystyle \begin{bmatrix}1&2&1\end{bmatrix}\begin{bmatrix}-1&0&1\\1&2&-1\\0&1&3\end{bmatrix}=\begin{bmatrix}1&5&2\end{bmatrix} \)
Then
\( \displaystyle \begin{bmatrix}1&5&2\end{bmatrix}\begin{bmatrix}2x\\x\\-7\end{bmatrix}=[\,2x+5x-14\,] \)
\( =[\,7x-14\,] \)
Setting this equal to [0],
\( 7x-14=0 \)
\( x=2 \)