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
Given the matrices: A = 1 & 3 & 4 \\ 2 & 1 & 1 \\ 1 & 3 & 4 B = -3 & -2 & 1 \\ 1 & 3 & 1 \\ 2 & -1 & 3 We need to find the product AB. Both A and B are 3 × 3 matrices, so the resulting matrix AB will also be a 3 × 3 matrix. Step 1: Calculate the elements for the first row of AB. Multiply the first row of A by each column of B. c_11 = (1 × -3) + (3 × 1) + (4 × 2) = -3 + 3 + 8 = 8 c_12 = (1 × -2) + (3 × 3) + (4 × -1) = -2 + 9 - 4 = 3 c_13 = (1 × 1) + (3 × 1) + (4 × 3) = 1 + 3 + 12 = 16 Step 2: Calculate the elements for the second row of AB. Multiply the second row of A by each column of B. c_21 = (2 × -3) + (1 × 1) + (1 × 2) = -6 + 1 + 2 = -3 c_22 = (2 × -2) + (1 × 3) + (1 × -1) = -4 + 3 - 1 = -2 c_23 = (2 × 1) + (1 × 1) + (1 × 3) = 2 + 1 + 3 = 6 Step 3: Calculate the elements for the third row of AB. Multiply the third row of A by each column of B. c_31 = (1 × -3) + (3 × 1) + (4 × 2) = -3 + 3 + 8 = 8 c_32 = (1 × -2) + (3 × 3) + (4 × -1) = -2 + 9 - 4 = 3 c_33 = (1 × 1) + (3 × 1) + (4 × 3) = 1 + 3 + 12 = 16 Step 4: Combine the calculated elements to form the product matrix AB. AB = 8 & 3 & 16 \\ -3 & -2 & 6 \\ 8 & 3 & 16 The product of the matrices is: 8 & 3 & 16 \\ -3 & -2 & 6 \\ 8 & 3 & 16 Last free one today — make it count tomorrow, or type /upgrade for unlimited.