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: Identify the given matrices A and B. From the image, the matrices are: A = 1 & 3 \\ 2 & 1 \\ 3 & 4 B = -3 & -2 & 1 \\ 1 & 3 & 1 Step 2: Determine the dimensions of the matrices and confirm multiplication is possible. Matrix A has dimensions 3 × 2 (3 rows, 2 columns). Matrix B has dimensions 2 × 3 (2 rows, 3 columns). Since the number of columns in A (2) equals the number of rows in B (2), the multiplication AB is possible. The resulting matrix will have dimensions 3 × 3. Step 3: Calculate the product AB. To find each element (AB)_ij, multiply the elements of the i-th row of A by the elements of the j-th column of B and sum the products. For the first row of AB: (AB)_11 = (1)(-3) + (3)(1) = -3 + 3 = 0 (AB)_12 = (1)(-2) + (3)(3) = -2 + 9 = 7 (AB)_13 = (1)(1) + (3)(1) = 1 + 3 = 4 For the second row of AB: (AB)_21 = (2)(-3) + (1)(1) = -6 + 1 = -5 (AB)_22 = (2)(-2) + (1)(3) = -4 + 3 = -1 (AB)_23 = (2)(1) + (1)(1) = 2 + 1 = 3 For the third row of AB: (AB)_31 = (3)(-3) + (4)(1) = -9 + 4 = -5 (AB)_32 = (3)(-2) + (4)(3) = -6 + 12 = 6 (AB)_33 = (3)(1) + (4)(1) = 3 + 4 = 7 Step 4: Write the resulting matrix AB. AB = 0 & 7 & 4 \\ -5 & -1 & 3 \\ -5 & 6 & 7 The final answer is 0 & 7 & 4 \\ -5 & -1 & 3 \\ -5 & 6 & 7 . Send me the next one 📸