If the matrix \(\begin{bmatrix}-1&x-y&4\\2&0&5\\x+y&z&6\end{bmatrix}\) is symmetric, then \(x + 3y+2z\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 16
A symmetric matrix has \(a_{ij} = a_{ji}\):
\( a_{12} = a_{21}:\ x - y = 2 \)
\( a_{13} = a_{31}:\ x + y = 4 \)
\( a_{23} = a_{32}:\ z = 5 \)
Adding the first two equations:
\( 2x = 6,\quad x = 3,\quad y = 1 \)
\( x + 3y + 2z = 3 + 3 + 10 = 16 \)