The problem gives two matrices, $P = \begin{bmatrix} 2 & 5 \\ -4 & 6 \end{bmatrix}$ and $Q = \begin{bmatrix} -2 & 0 \\ -1 & 7 \end{bmatrix}$. The problem asks to find $P=2Q$. However, this is wrong, the question should be find matrix $R$, where $R = P - 2Q$.

1. Problem Description

The problem gives two matrices, $P = \begin{bmatrix} 2 & 5 \\ -4 & 6 \end{bmatrix}$ and $Q = \begin{bmatrix} -2 & 0 \\ -1 & 7 \end{bmatrix}$. The problem asks to find $P=2Q$. However, this is wrong, the question should be find matrix $R$, where $R = P - 2Q$.

2. Solution Steps

First, we need to calculate $2Q$:

$2Q = 2 \begin{bmatrix} -2 & 0 \\ -1 & 7 \end{bmatrix} = \begin{bmatrix} 2(-2) & 2(0) \\ 2(-1) & 2(7) \end{bmatrix} = \begin{bmatrix} -4 & 0 \\ -2 & 14 \end{bmatrix}$.

Next, we calculate $R = P - 2Q$:

$R = \begin{bmatrix} 2 & 5 \\ -4 & 6 \end{bmatrix} - \begin{bmatrix} -4 & 0 \\ -2 & 14 \end{bmatrix} = \begin{bmatrix} 2 - (-4) & 5 - 0 \\ -4 - (-2) & 6 - 14 \end{bmatrix} = \begin{bmatrix} 2 + 4 & 5 \\ -4 + 2 & -8 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ -2 & -8 \end{bmatrix}$.

3. Final Answer

$R = \begin{bmatrix} 6 & 5 \\ -2 & -8 \end{bmatrix}$