![Given that A = [[1, 4], [2, 5]] and B = [[1, 1], [0, 2]]. Evaluate (I) AB (II) BA](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1781006369562-87a153543041f486.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 & 4 \\ 2 & 5 and B = 1 & 1 \\ 0 & 2 I) Evaluate AB Step 1: Set up the multiplication for AB. AB = 1 & 4 \\ 2 & 5 1 & 1 \\ 0 & 2 Step 2: Perform the matrix multiplication. To find each element of AB, multiply the rows of A by the columns of B. AB = (1)(1) + (4)(0) & (1)(1) + (4)(2) \\ (2)(1) + (5)(0) & (2)(1) + (5)(2) Step 3: Calculate the values for each element. AB = 1 + 0 & 1 + 8 \\ 2 + 0 & 2 + 10 Step 4: Simplify to get the final matrix for AB. AB = 1 & 9 \\ 2 & 12 II) Evaluate BA Step 1: Set up the multiplication for BA. BA = 1 & 1 \\ 0 & 2 1 & 4 \\ 2 & 5 Step 2: Perform the matrix multiplication. To find each element of BA, multiply the rows of B by the columns of A. BA = (1)(1) + (1)(2) & (1)(4) + (1)(5) \\ (0)(1) + (2)(2) & (0)(4) + (2)(5) Step 3: Calculate the values for each element. BA = 1 + 2 & 4 + 5 \\ 0 + 4 & 0 + 10 Step 4: Simplify to get the final matrix for BA. BA = 3 & 9 \\ 4 & 10 Drop the next question 📸