If \[ \begin{bmatrix} 1 & 3 \\ 4 & 5 \end{bmatrix} \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}, \] then the value of \( x \) is:
- -1
- 0
- 1
- 3
The Correct Option is A
Solution and Explanation
Perform the matrix multiplication:
\[ \begin{bmatrix} 1 & 3 \\ 4 & 5 \end{bmatrix} \cdot \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} 1 \cdot x + 3 \cdot 2 \\ 4 \cdot x + 5 \cdot 2 \end{bmatrix} = \begin{bmatrix} x + 6 \\ 4x + 10 \end{bmatrix}. \]
Equating this with \(\begin{bmatrix} 5 \\ 6 \end{bmatrix}\), solve:
\[ x + 6 = 5 \implies x = -1, \]
\[ 4x + 10 = 6 \implies 4x = -4 \implies x = -1. \]
Both equations confirm \(x = -1\).
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