If \(A=\begin{bmatrix}-1 & 1 & 4\\1 & 5 & 7\\4 & 7 & 8\end{bmatrix}\), then \(2A + 7A'\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9A
The entries placed symmetrically about the leading diagonal are equal:
\( a_{12} = a_{21} = 1,\quad a_{13} = a_{31} = 4,\quad a_{23} = a_{32} = 7 \)
So interchanging rows and columns gives the same matrix: A is symmetric, \(A' = A\). Hence
\( 2A + 7A' = 2A + 7A = 9A \)