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 product PQ. To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix. PQ = 2 & 4 \\ -9 & 1 1 & -1 \\ 3 & -2 PQ = (2)(1) + (4)(3) & (2)(-1) + (4)(-2) \\ (-9)(1) + (1)(3) & (-9)(-1) + (1)(-2) PQ = 2 + 12 & -2 - 8 \\ -9 + 3 & 9 - 2 PQ = 14 & -10 \\ -6 & 7 Step 2: Calculate 2Q. To multiply a matrix by a scalar, multiply each element in the matrix by the scalar. 2Q = 2 1 & -1 \\ 3 & -2 2Q = 2 × 1 & 2 × (-1) \\ 2 × 3 & 2 × (-2) 2Q = 2 & -2 \\ 6 & -4 Step 3: Calculate PQ + 2Q. To add matrices, add the corresponding elements. PQ + 2Q = 14 & -10 \\ -6 & 7 + 2 & -2 \\ 6 & -4 PQ + 2Q = 14+2 & -10+(-2) \\ -6+6 & 7+(-4) PQ + 2Q = 16 & -12 \\ 0 & 3 The final answer is 16 & -12 \\ 0 & 3 . Send me the next one 📸