If \(\begin{bmatrix}1 & 3\\ 4 & 5\end{bmatrix}\begin{bmatrix}x\\ 2\end{bmatrix}=\begin{bmatrix}5\\ 6\end{bmatrix}\), then value of x is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −1
Multiplying the matrices (row by column):
\( \displaystyle \begin{bmatrix}1 & 3\\ 4 & 5\end{bmatrix}\begin{bmatrix}x\\ 2\end{bmatrix} = \begin{bmatrix}x + 6\\ 4x + 10\end{bmatrix} \)
Equating with \(\begin{bmatrix}5\\ 6\end{bmatrix}\), the corresponding entries are equal:
\(x + 6 = 5,\quad x = -1\)
\(4x + 10 = 6,\quad x = -1\)
Both rows give the same value, so x = −1.