Given that P = [[2, 1], [5, -3]] and Q = [[4, -8], [1, -2]], find (2P - Q).

To find $2P - Q$, we first multiply matrix $P$ by 2, and then subtract matrix $Q$ from the result.

Given matrices: $P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}$ $Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}$

Step 1: Calculate $2P$. Multiply each element of matrix $P$ by 2. $2P = 2 \times \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 2 \times 2 & 2 \times 1 \\ 2 \times 5 & 2 \times (-3) \end{pmatrix} = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}$

Step 2: Calculate $2P - Q$. Subtract the corresponding elements of matrix $Q$ from $2P$. $2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}$ $2P - Q = \begin{pmatrix} 4 - 4 & 2 - (-8) \\ 10 - 1 & -6 - (-2) \end{pmatrix}$ $2P - Q = \begin{pmatrix} 0 & 2 + 8 \\ 9 & -6 + 2 \end{pmatrix}$ $2P - Q = \begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}$

Step 3: Compare the result with the given options. The calculated matrix $\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}$ matches option D.

The final answer is $\boxed{D}$. That's 2 down. 3 left today — send the next one.