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
You're on a roll — Given the matrices: B = 1 & 2 \\ 3 & 4 \\ 5 & 6 A = 1 & 2 & 3 \\ 4 & 5 & 6 We need to find the product BA. Matrix B is a 3 × 2 matrix and Matrix A is a 2 × 3 matrix. The resulting matrix BA will be a 3 × 3 matrix. Step 1: Calculate the elements for the first row of BA. Multiply the first row of B by each column of A. (1 × 1) + (2 × 4) = 1 + 8 = 9 (element c_11) (1 × 2) + (2 × 5) = 2 + 10 = 12 (element c_12) (1 × 3) + (2 × 6) = 3 + 12 = 15 (element c_13) Step 2: Calculate the elements for the second row of BA. Multiply the second row of B by each column of A. (3 × 1) + (4 × 4) = 3 + 16 = 19 (element c_21) (3 × 2) + (4 × 5) = 6 + 20 = 26 (element c_22) (3 × 3) + (4 × 6) = 9 + 24 = 33 (element c_23) Step 3: Calculate the elements for the third row of BA. Multiply the third row of B by each column of A. (5 × 1) + (6 × 4) = 5 + 24 = 29 (element c_31) (5 × 2) + (6 × 5) = 10 + 30 = 40 (element c_32) (5 × 3) + (6 × 6) = 15 + 36 = 51 (element c_33) Step 4: Combine the calculated elements to form the product matrix BA. BA = 9 & 12 & 15 \\ 19 & 26 & 33 \\ 29 & 40 & 51 The product of the matrices is: 9 & 12 & 15 \\ 19 & 26 & 33 \\ 29 & 40 & 51 What's next?