Question

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:

• A. -1
• B. 0
• C. 1
• D. 3

Answer 1

Answer: (A)

-1

Answer 2

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 $x = -1$.