![Given matrices A = [[1, 2, 3], [4, 3, 6]] and B = [[1, 2], [3, 4], [5, 6]], calculate the product AB.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1779544835822-12972720ec7da17d.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
Given the matrices: A = 1 & 2 & 3 \\ 4 & 3 & 6 B = 1 & 2 \\ 3 & 4 \\ 5 & 6 We need to find the product AB. Matrix A is a 2 × 3 matrix and Matrix B is a 3 × 2 matrix. The resulting matrix AB will be a 2 × 2 matrix. Step 1: Calculate the element in the first row, first column of AB. Multiply the first row of A by the first column of B. (1 × 1) + (2 × 3) + (3 × 5) = 1 + 6 + 15 = 22 Step 2: Calculate the element in the first row, second column of AB. Multiply the first row of A by the second column of B. (1 × 2) + (2 × 4) + (3 × 6) = 2 + 8 + 18 = 28 Step 3: Calculate the element in the second row, first column of AB. Multiply the second row of A by the first column of B. (4 × 1) + (3 × 3) + (6 × 5) = 4 + 9 + 30 = 43 Step 4: Calculate the element in the second row, second column of AB. Multiply the second row of A by the second column of B. (4 × 2) + (3 × 4) + (6 × 6) = 8 + 12 + 36 = 56 Step 5: Combine the calculated elements to form the product matrix AB. AB = 22 & 28 \\ 43 & 56 The product of the matrices is: 22 & 28 \\ 43 & 56 3 done, 2 left today. You're making progress.