If P = \(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) and Q = \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\), find 2P + Q
A
\(\begin{vmatrix} 7 & 7 \\ 14 & 8 \end{vmatrix}\)
B
\(\begin{vmatrix} 14 & 8 \\ 7 & 7 \end{vmatrix}\)
C
\(\begin{vmatrix} 7 & 7 \\ 8 & 14 \end{vmatrix}\)
D
\(\begin{vmatrix} 8 & 14 \\ 7 & 7 \end{vmatrix}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
2P + Q = 2\(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)
= \(\begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)
= \(\begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}\)
Source: Myschool Past Questions Archive (Record #27056)