Question

If $A = \begin{bmatrix} 4 & x + 2 \\ 2x - 3 & x + 1 \end{bmatrix}$is symmetric, then x =

• A. 3
• B. 5
• C. 2
• D. 4

Answer 1

Answer: (B)

5

Answer 2

For symmetric matrix, $A = A^{T}$

⇒ $\begin{bmatrix} 4 & 2x - 3 \\ x + 2 & x + 1 \end{bmatrix} = \begin{bmatrix} 4 & x + 2 \\ 2x - 3 & x + 1 \end{bmatrix}$ ⇒ $2x - 3 = x + 2$

⇒ $x = 5$