Given matrix M = \(\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}\), find \(M^{T} + 2M\)
A. \(\begin{vmatrix} -4 & 2 & 1\\ 6 & 0 & 5 \\ 0 & 6 & 2 \end{vmatrix}\)
B. \(\begin{vmatrix} -6 & 0 & 13\\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)
C. \(\begin{vmatrix} 5 & 2 & 6 \\ 0 & 1 & 1\\ 3 & 4 & -7 \end{vmatrix}\)
D. \(\begin{vmatrix} -4 & 0 & 8 \\ 0 & -2 & -16 \\ 10 & 12 & 6 \end{vmatrix}\)
Correct Answer: B
Explanation
M = \(\begin{vmatrix} -2 & 0 & 4 \\ 0 & -1 & 6 \\ 5 & 6 & 3 \end{vmatrix}\)
M\(^{T}\) = \(\begin{vmatrix} -2 & 0 & 5 \\ 0 & -1 & 6\\ 4 & 6 & 3 \end{vmatrix}\)
2M = \(\begin{vmatrix} -4 & 0 & 8\\ 0 & -2 & 12\\ 10 & 12 & 6\end{vmatrix}\)
M\(^T\) + 2M = \(\begin{vmatrix} -6 & 0 & 13 \\ 0 & -3 & 18 \\ 14 & 18 & 9 \end{vmatrix}\)
