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
Step 1: Calculate the first element of the resulting matrix, c_1,1. This is obtained by multiplying the elements of the first row of the first matrix by the corresponding elements of the column vector and summing them. c_1,1 = (6)(4) + (2)(-2) + (4)(1) c_1,1 = 24 - 4 + 4 c_1,1 = 24 Step 2: Calculate the second element of the resulting matrix, c_2,1. This is obtained by multiplying the elements of the second row of the first matrix by the corresponding elements of the column vector and summing them. c_2,1 = (-1)(4) + (4)(-2) + (3)(1) c_2,1 = -4 - 8 + 3 c_2,1 = -12 + 3 c_2,1 = -9 Step 3: Calculate the third element of the resulting matrix, c_3,1. This is obtained by multiplying the elements of the third row of the first matrix by the corresponding elements of the column vector and summing them. c_3,1 = (-2)(4) + (9)(-2) + (3)(1) c_3,1 = -8 - 18 + 3 c_3,1 = -26 + 3 c_3,1 = -23 Step 4: Assemble the resulting matrix. Ax = c_1,1 \\ c_2,1 \\ c_3,1 = 24 \\ -9 \\ -23 The final answer is 24 \\ -9 \\ -23 .