Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).
Question 1 Report
Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).
Answer Details
To find the value of (2P - Q), we first need to compute 2P and Q, and then subtract Q from 2P.
To compute 2P, we multiply each element of matrix P by 2:
2P = \(\begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}\)
To subtract Q from 2P, we subtract each corresponding element of matrix Q from matrix 2P:
2P - Q = \(\begin{pmatrix} 4-4 & 2+8 \\ 10-1 & -6+2 \end{pmatrix}\)
= \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)
Therefore, the answer is \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\).
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