The value of k for which the matrix \(\begin{pmatrix} 0 & 2 & k \\ 2 & 0 & 5 \\ -3 & 5 & 0 \end{pmatrix}\) is a symmetric matrix is given by:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −3
A matrix is symmetric when \(\mathrm{A}^{T} = \mathrm{A}\), that is, \(a_{ij} = a_{ji}\) for every i, j.
\(a_{12} = a_{21} = 2\)
\(a_{23} = a_{32} = 5\)
\(a_{13} = a_{31}\) gives \(k = -3\)