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 = 2 & 4 & 3 & 6 \\ 2 & 1 & 3 & 1 B = 1 & 1 & 1 & 1 \\ 2 & 2 & 2 & 2 We need to find 3A + 2B. Step 1: Calculate 3A by multiplying each element of matrix A by 3. 3A = 3 × 2 & 4 & 3 & 6 \\ 2 & 1 & 3 & 1 = 3 × 2 & 3 × 4 & 3 × 3 & 3 × 6 \\ 3 × 2 & 3 × 1 & 3 × 3 & 3 × 1 3A = 6 & 12 & 9 & 18 \\ 6 & 3 & 9 & 3 Step 2: Calculate 2B by multiplying each element of matrix B by 2. 2B = 2 × 1 & 1 & 1 & 1 \\ 2 & 2 & 2 & 2 = 2 × 1 & 2 × 1 & 2 × 1 & 2 × 1 \\ 2 × 2 & 2 × 2 & 2 × 2 & 2 × 2 2B = 2 & 2 & 2 & 2 \\ 4 & 4 & 4 & 4 Step 3: Add the resulting matrices 3A and 2B by adding their corresponding elements. 3A + 2B = 6 & 12 & 9 & 18 \\ 6 & 3 & 9 & 3 + 2 & 2 & 2 & 2 \\ 4 & 4 & 4 & 4 3A + 2B = 6+2 & 12+2 & 9+2 & 18+2 \\ 6+4 & 3+4 & 9+4 & 3+4 Step 4: Perform the addition for each element. 3A + 2B = 8 & 14 & 11 & 20 \\ 10 & 7 & 13 & 7 The result of 3A + 2B is: 8 & 14 & 11 & 20 \\ 10 & 7 & 13 & 7 That's 2 down. 3 left today — send the next one.