If \(\begin{bmatrix}x&2&0\end{bmatrix}\begin{bmatrix}5\\-1\\x\end{bmatrix} = \begin{bmatrix}3&1\end{bmatrix}\begin{bmatrix}-2\\x\end{bmatrix}\), then the value of \(x\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(-1\)
Each side is a row matrix times a column matrix, so each product is a \(1 \times 1\) matrix.
Left side:
\(x(5) + 2(-1) + 0(x) = 5x - 2\)
Right side:
\(3(-2) + 1(x) = x - 6\)
By equality of matrices:
\(5x - 2 = x - 6\)
\(4x = -4\)
\(x = -1\)