![Calculate the product of matrices X and Y: X = [[1, 2], [3, 4]], Y = [[5, 6], [7, 8]]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777152486619-5a7a94d69ff9d2d7.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 the product of matrices X and Y, we perform matrix multiplication. Given matrices: X = 1 & 2 \\ 3 & 4 Y = 5 & 6 \\ 7 & 8 Step 1: Calculate the element in the first row, first column of XY. Multiply the first row of X by the first column of Y: (1 × 5) + (2 × 7) = 5 + 14 = 19 Step 2: Calculate the element in the first row, second column of XY. Multiply the first row of X by the second column of Y: (1 × 6) + (2 × 8) = 6 + 16 = 22 Step 3: Calculate the element in the second row, first column of XY. Multiply the second row of X by the first column of Y: (3 × 5) + (4 × 7) = 15 + 28 = 43 Step 4: Calculate the element in the second row, second column of XY. Multiply the second row of X by the second column of Y: (3 × 6) + (4 × 8) = 18 + 32 = 50 Step 5: Combine the calculated elements to form the product matrix XY. XY = 19 & 22 \\ 43 & 50 Comparing this result with the given options: a. 19 & 26 \\ 11 & 18 b. 11 & 18 \\ 15 & 22 c. 19 & 22 \\ 43 & 50 d. 11 & 14 \\ 15 & 18 The calculated product matches option c. The final answer is c. 19 & 22 \\ 43 & 50 . 3 done, 2 left today. You're making progress.