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
Let's look at some examples of determinants. Example 1: 2x2 Matrix Consider the matrix: A = [[3, 5], [1, 4]] Step 1: Apply the formula for a 2x2 determinant: det(A) = ad - bc det(A) = (3 × 4) - (5 × 1) Step 2: Calculate the result. det(A) = 12 - 5 det(A) = 7 The determinant of matrix A is 7. Example 2: 3x3 Matrix Consider the matrix: B = [[1, 2, 3], [0, 4, 5], [1, 0, 6]] Step 1: Apply the formula for a 3x3 determinant: det(B) = a(ei - fh) - b(di - fg) + c(dh - eg) det(B) = 1 × ((4 × 6) - (5 × 0)) - 2 × ((0 × 6) - (5 × 1)) + 3 × ((0 × 0) - (4 × 1)) Step 2: Simplify the terms inside the parentheses. det(B) = 1 × (24 - 0) - 2 × (0 - 5) + 3 × (0 - 4) Step 3: Perform the multiplications. det(B) = 1 × 24 - 2 × (-5) + 3 × (-4) det(B) = 24 + 10 - 12 Step 4: Calculate the final result. det(B) = 34 - 12 det(B) = 22 The determinant of matrix B is 22. That's 2 down. 3 left today — send the next one.