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
Step 1: Identify the given matrices M and N. M = 1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 N = 1 & -2 & 3 \\ 4 & -1 & 5 \\ 2 & -3 & -1 Step 2: Calculate 2M. Multiply each element of matrix M by 2: 2M = 2 1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 = 2 × 1 & 2 × 3 & 2 × 2 \\ 2 × 4 & 2 × 5 & 2 × (-1) \\ 2 × (-3) & 2 × 2 & 2 × 0 2M = 2 & 6 & 4 \\ 8 & 10 & -2 \\ -6 & 4 & 0 Step 3: Calculate 3N. Multiply each element of matrix N by 3: 3N = 3 1 & -2 & 3 \\ 4 & -1 & 5 \\ 2 & -3 & -1 = 3 × 1 & 3 × (-2) & 3 × 3 \\ 3 × 4 & 3 × (-1) & 3 × 5 \\ 3 × 2 & 3 × (-3) & 3 × (-1) 3N = 3 & -6 & 9 \\ 12 & -3 & 15 \\ 6 & -9 & -3 Step 4: Evaluate 2M - 3N. Subtract the corresponding elements of 3N from 2M: 2M - 3N = 2 & 6 & 4 \\ 8 & 10 & -2 \\ -6 & 4 & 0 - 3 & -6 & 9 \\ 12 & -3 & 15 \\ 6 & -9 & -3 2M - 3N = 2 - 3 & 6 - (-6) & 4 - 9 \\ 8 - 12 & 10 - (-3) & -2 - 15 \\ -6 - 6 & 4 - (-9) & 0 - (-3) 2M - 3N = -1 & 6 + 6 & -5 \\ -4 & 10 + 3 & -17 \\ -12 & 4 + 9 & 0 + 3 2M - 3N = -1 & 12 & -5 \\ -4 & 13 & -17 \\ -12 & 13 & 3 Step 5: Compare the result with the given options. The calculated matrix matches option D. The final answer is -1 & 12 & -5 \\ -4 & 13 & -17 \\ -12 & 13 & 3 . That's 2 down. 3 left today — send the next one.