![Given that Q = [[2, 1, 3], [2, 1, 2], [1, 2, 1]], find |Q|. Evaluate A⁻¹ x A.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1782909689887-3de81b1170e995f5.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
Here's how to find the determinant of matrix Q: Step 1: Write down the given matrix Q. Q = 2 & 3 & 1 \\ 3 & 1 & 2 \\ 2 & 2 & 1 Step 2: Use the cofactor expansion method to find the determinant |Q|. For a 3 × 3 matrix a & b & c \\ d & e & f \\ g & h & i , the determinant is given by a(ei - fh) - b(di - fg) + c(dh - eg). Applying this formula to matrix Q: |Q| = 2 1 & 2 \\ 2 & 1 - 3 3 & 2 \\ 2 & 1 + 1 3 & 1 \\ 2 & 2 Step 3: Calculate the determinants of the 2 × 2 sub-matrices. • For the first term: 1 & 2 \\ 2 & 1 = (1 × 1) - (2 × 2) = 1 - 4 = -3 • For the second term: 3 & 2 \\ 2 & 1 = (3 × 1) - (2 × 2) = 3 - 4 = -1 • For the third term: 3 & 1 \\ 2 & 2 = (3 × 2) - (1 × 2) = 6 - 2 = 4 Step 4: Substitute these values back into the expression for |Q| and simplify. |Q| = 2(-3) - 3(-1) + 1(4) |Q| = -6 + 3 + 4 |Q| = -6 + 7 |Q| = 1 Part (ii) of the question is incomplete in the image provided. That's 2 down. 3 left today — send the next one.