If matrix \( A=\begin{bmatrix}0 & 3a & -4\\2 & 1 & 2\\2b & 2 & -1\end{bmatrix} \) is a symmetric matrix, then the values of \( a \) and \( b \) are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( a=2/3,b=-2 \)
A is symmetric when \( A'=A \), that is \( a_{ij}=a_{ji} \) for all i, j:
\( \displaystyle a_{12}=a_{21}:\ 3a=2\ \Rightarrow\ a=\frac{2}{3} \)
\( \displaystyle a_{13}=a_{31}:\ -4=2b\ \Rightarrow\ b=-2 \)
\( \displaystyle a_{23}=a_{32}:\ 2=2\ \text{(already true)} \)
So \( a=\frac{2}{3} \) and \( b=-2 \).