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 matrix A. The matrix A is a 3 × 3 matrix: A = -2 & 3 & 1 \\ 2 & -1 & 3 \\ 1 & 2 & 1 Step 2: Calculate the determinant using cofactor expansion along the first row. The formula for the determinant of a 3 × 3 matrix a & b & c \\ d & e & f \\ g & h & i is a(ei - fh) - b(di - fg) + c(dh - eg). Step 3: Substitute the values from matrix A into the determinant formula. (A) = -2 -1 & 3 \\ 2 & 1 - 3 2 & 3 \\ 1 & 1 + 1 2 & -1 \\ 1 & 2 Step 4: Calculate the 2 × 2 determinants. -1 & 3 \\ 2 & 1 = (-1)(1) - (3)(2) = -1 - 6 = -7 2 & 3 \\ 1 & 1 = (2)(1) - (3)(1) = 2 - 3 = -1 2 & -1 \\ 1 & 2 = (2)(2) - (-1)(1) = 4 - (-1) = 4 + 1 = 5 Step 5: Substitute these values back into the expression for (A) and simplify. (A) = -2(-7) - 3(-1) + 1(5) (A) = 14 + 3 + 5 (A) = 22 The final answer is 22. That's 2 down. 3 left today — send the next one.