Given that M = \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\) and N = \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\), calculate (3M - 2N)
A. \(\begin{pmatrix} 1 & 6 \\ 1 & 18 \end{pmatrix}\)
B. \(\begin{pmatrix} -1 & -6 \\ 1 & 18 \end{pmatrix}\)
C. \(\begin{pmatrix} 1 & 6 \\ -1 & -18 \end{pmatrix}\)
D. \(\begin{pmatrix} -1 & -6 \\ -1 & -18 \end{pmatrix}\)
Correct Answer: B
Explanation
3M = 3 \(\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}\)
= \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\)
2N = 2 \(\begin{pmatrix} 5 & 6 \\ -2 & -3 \end{pmatrix}\)
= \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)
(3M - 2N) = \(\begin{pmatrix} 9 & 6 \\ -3 & 12 \end{pmatrix}\) - \(\begin{pmatrix} 10 & 12 \\ -4 & -6 \end{pmatrix}\)
