![Multiply matrices A and B, where A = [[2, 1, -1], [0, 3, 2]] and B = [[1, 0], [3, -1], [-1, 2]].](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1778845756696-5bf126f7fa217aff.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
Alright, Hurry, let's multiply these matrices. We are given two matrices: A = 2 & 1 & -1 \\ 0 & 3 & 2 B = 1 & 0 \\ 3 & -1 \\ -1 & 2 To find the product AB, we multiply the rows of matrix A by the columns of matrix B. The resulting matrix will be a 2 × 2 matrix. Step 1: Calculate the element in the first row, first column (c_11). Multiply the first row of A by the first column of B: c_11 = (2)(1) + (1)(3) + (-1)(-1) c_11 = 2 + 3 + 1 = 6 Step 2: Calculate the element in the first row, second column (c_12). Multiply the first row of A by the second column of B: c_12 = (2)(0) + (1)(-1) + (-1)(2) c_12 = 0 - 1 - 2 = -3 Step 3: Calculate the element in the second row, first column (c_21). Multiply the second row of A by the first column of B: c_21 = (0)(1) + (3)(3) + (2)(-1) c_21 = 0 + 9 - 2 = 7 Step 4: Calculate the element in the second row, second column (c_22). Multiply the second row of A by the second column of B: c_22 = (0)(0) + (3)(-1) + (2)(2) c_22 = 0 - 3 + 4 = 1 Step 5: Form the product matrix AB. AB = c_11 & c_12 \\ c_21 & c_22 = 6 & -3 \\ 7 & 1 The product AB is 6 & -3 \\ 7 & 1 . 3 done, 2 left today. You're making progress.