Question

If $\begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} \begin{bmatrix} 1 & -3 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} -4 & 6 \\ -9 & x \end{bmatrix}$, then the value of $x$ is:

• A. 13
• B. -13
• C. 9
• D. 5

Hint:

Matrix multiplication is row-by-column; verify each element carefully.

Answer 1

The Correct Option is B

Multiply the two matrices: \[ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix} \begin{bmatrix} 1 & -3 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} 2 \times 1 + 3 \times (-2) & 2 \times (-3) + 3 \times 4 \\ 5 \times 1 + 7 \times (-2) & 5 \times (-3) + 7 \times 4 \end{bmatrix} \] Calculate each element: \[ a_{11} = 2 - 6 = -4 \] \[ a_{12} = -6 + 12 = 6 \] \[ a_{21} = 5 - 14 = -9 \] \[ a_{22} = -15 + 28 = 13 \] Given matrix on right side is: \[ \begin{bmatrix} -4 & 6 \\ -9 & x \end{bmatrix} \] Equate: \[ x = 13 \] But 13 is option (A). However, the question's options include -13 too. Check for sign error: The multiplication yields \(x = 13\), but the given options include -13. Rechecking: \[ a_{22} = 5 \times (-3) + 7 \times 4 = -15 + 28 = 13 \] So the value of \(x = 13\).