Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).
A. \(\begin{pmatrix} -6 & 17 \\ 3 & 1 \end{pmatrix}\)
B. \(\begin{pmatrix} -2 & 9 \\ 4 & 1 \end{pmatrix}\)
C. \(\begin{pmatrix} 0 & -6 \\ 9 & -8 \end{pmatrix}\)
D. \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)
Correct Answer: D
Explanation
\(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} ; Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)
\(2P = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}\)
\(2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)
= \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)
