If the matrix \( \begin{bmatrix}5 & x^2\\3x-2 & x-1\end{bmatrix} \) is symmetric, then values of \( x \) are :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 and 2
A matrix is symmetric when \( a_{ij}=a_{ji} \), that is, \( A^{T}=A \). Here the off-diagonal entries must be equal:
\( \displaystyle x^2=3x-2 \)
\( \displaystyle x^2-3x+2=0 \)
\( \displaystyle (x-1)(x-2)=0 \)
So x = 1 or x = 2.
Shortcut: Put the options into \( x^2=3x-2 \): x = 1 gives 1 = 1 and x = 2 gives 4 = 4, while x = 0, 3 and 5 fail.