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: Write down the given matrix P. P = 4 & 3 \\ 1 & 2 Step 2: Calculate P^2 by multiplying P by P. P^2 = P × P = 4 & 3 \\ 1 & 2 4 & 3 \\ 1 & 2 Step 3: Perform the matrix multiplication. To find the element in row i and column j of the product matrix, multiply the elements of row i of the first matrix by the corresponding elements of column j of the second matrix and sum the products. • Top-left element (row 1, column 1): (4 × 4) + (3 × 1) = 16 + 3 = 19 • Top-right element (row 1, column 2): (4 × 3) + (3 × 2) = 12 + 6 = 18 • Bottom-left element (row 2, column 1): (1 × 4) + (2 × 1) = 4 + 2 = 6 • Bottom-right element (row 2, column 2): (1 × 3) + (2 × 2) = 3 + 4 = 7 Step 4: Construct the resulting matrix P^2. P^2 = 19 & 18 \\ 6 & 7 The final answer is 19 & 18 \\ 6 & 7 .