If A = \( \begin{bmatrix}-1 & 2 & 3x\\2y & 4 & -1\\6 & 5 & 0\end{bmatrix} \) is a symmetric matrix, then the value of \( 2x+3y \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7
A matrix is symmetric when \( \mathrm{A}^{\mathrm{T}}=\mathrm{A} \), that is, \( a_{ij}=a_{ji} \) for every i and j.
\( \displaystyle a_{21}=a_{12}:\ 2y=2\ \Rightarrow\ y=1 \)
\( \displaystyle a_{13}=a_{31}:\ 3x=6\ \Rightarrow\ x=2 \)
\( \displaystyle 2x+3y=2(2)+3(1) \)
\( \displaystyle =4+3=7 \)
Note: It seems that there is a mistake in the original NTA paper, which prints \( a_{23}=-1 \) and \( a_{32}=5 \), when these two entries should be equal, because a symmetric matrix needs \( a_{23}=a_{32} \). These entries do not contain x or y, so the question can still be solved from the other two pairs of entries.