Question

If A = $\begin{bmatrix} 1 & 12 & 4y \\ 6x & 5 & 2x \\ 8x & 4 & 6 \end{bmatrix}$ is a symmetric matrix, then (2x + y) is

• A. -8
• B. 0
• C. 6
• D. 8

Answer 1

Answer: (D)

8

Answer 2

A matrix is symmetric if its transpose is equal to itself ($A = A^T$), meaning $a_{ij} = a_{ji}$. For the given matrix, this condition implies $12 = 6x$, $4y = 8x$, and $2x = 4$. Solving these equations yields $x=2$ and $y=4$. Substituting these values into $(2x+y)$ gives $2(2)+4=8$.