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