Let \(A = \begin{bmatrix} 1 & a & 0 \\ 2 & 3 & c \\ b & -1 & 6\end{bmatrix}\)
be a symmetric matrix. What is \(a + b + c\)?
The answer is \(1\).
Since \(A\) is symmetric, we must have
\(A = \begin{bmatrix} 1 & 2 & 0 \\ 2 & 3 & -1 \\ 0 & -1 & 6\end{bmatrix}.\)
Hence,
\(a + b + c = 2 + 0 + (-1) = 1\).