![Evaluate the determinant of the matrix below: [[0, 4, 7], [1, 5, 8], [3, 6, 9]]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1782402993609-cc05f6557574a67f.png&w=3840&q=75)
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. The matrix is: A = 0 & 4 & 7 \\ 1 & 5 & 8 \\ 3 & 6 & 9 Step 2: Use the cofactor expansion method to evaluate the determinant. We will expand 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). (A) = 0 · 5 & 8 \\ 6 & 9 - 4 · 1 & 8 \\ 3 & 9 + 7 · 1 & 5 \\ 3 & 6 Step 3: Calculate the 2 × 2 determinants. For the first term: 0 · ((5 × 9) - (8 × 6)) = 0 · (45 - 48) = 0 · (-3) = 0 For the second term: -4 · ((1 × 9) - (8 × 3)) = -4 · (9 - 24) = -4 · (-15) = 60 For the third term: 7 · ((1 × 6) - (5 × 3)) = 7 · (6 - 15) = 7 · (-9) = -63 Step 4: Sum the results to find the determinant. (A) = 0 + 60 - 63 (A) = -3 The determinant of the matrix is: -3 Last free one today — make it count tomorrow, or type /upgrade for unlimited.