![Given that P = [[2, 1], [5, -3]] and Q = [[4, -8], [1, -2]], find (2P - Q).](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1781732103629-7f723a0fc3e60c62.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find 2P - Q, we first multiply matrix P by 2, and then subtract matrix Q from the result. Given matrices: P = 2 & 1 \\ 5 & -3 Q = 4 & -8 \\ 1 & -2 Step 1: Calculate 2P. Multiply each element of matrix P by 2. 2P = 2 × 2 & 1 \\ 5 & -3 = 2 × 2 & 2 × 1 \\ 2 × 5 & 2 × (-3) = 4 & 2 \\ 10 & -6 Step 2: Calculate 2P - Q. Subtract the corresponding elements of matrix Q from 2P. 2P - Q = 4 & 2 \\ 10 & -6 - 4 & -8 \\ 1 & -2 2P - Q = 4 - 4 & 2 - (-8) \\ 10 - 1 & -6 - (-2) 2P - Q = 0 & 2 + 8 \\ 9 & -6 + 2 2P - Q = 0 & 10 \\ 9 & -4 Step 3: Compare the result with the given options. The calculated matrix 0 & 10 \\ 9 & -4 matches option D. The final answer is D. That's 2 down. 3 left today — send the next one.