Evaluate \(\begin{pmatrix}3 & -2 \\-7 & 5 \end{pmatrix}\) + 2\(\begin{pmatrix}-2 & 4\\3 & -1 \end{pmatrix}\)
A
\(\begin{pmatrix}-1 & 6 \\-1 & 3 \end{pmatrix}\)
B
\(\begin{pmatrix}3 & 4 \\-2 & 6 \end{pmatrix}\)
C
\(\begin{pmatrix}-1 & 6 \\1 & 3 \end{pmatrix}\)
D
\(\begin{pmatrix}3 & 4 \\2 & 6 \end{pmatrix}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\begin{pmatrix}3 & -2 \\ -7 & 5 \end{pmatrix} + 2 \begin{pmatrix}-2 & 4 \\ 3 & -1 \end{pmatrix}\)
\(2 \begin{pmatrix}-2 & 4 \\ 3 & -1 \end{pmatrix} = \begin{pmatrix}2 \cdot -2 & 2 \cdot 4 \\ 2 \cdot 3 & 2 \cdot -1\end{pmatrix} = \begin{pmatrix}-4 & 8 \\ 6 & -2\end{pmatrix}\)
\(\begin{pmatrix}3 & -2 \\ -7 & 5 \end{pmatrix} + \begin{pmatrix}-4 & 8 \\ 6 & -2\end{pmatrix} = \begin{pmatrix}3 + (-4) & -2 + 8 \\ -7 + 6 & 5 + (-2)\end{pmatrix}\)
\(= \begin{pmatrix}-1 & 6 \\ -1 & 3\end{pmatrix}\)
Thus, the final result is:
\(\begin{pmatrix}-1 & 6 \\ -1 & 3\end{pmatrix}\)
Source: Myschool Past Questions Archive (Record #72043)