Inverse of a square matrix
Matrices and determinants (introductory) · Mathematics
Study notes
Q: Find the inverse of A = [[2,1],[1,1]]. Use it to solve 2x + y = 5, x + y = 3. Step 1: det = 2×1 - 1×1 = 1. A⁻¹ = [[1,-1],[-1,2]]. Step 2: [x;y] = A⁻¹[5;3] = [5-3; -5+6] = [2;1]. Step 3: Check: 2(2)+1 = 5 ✓, 2+1 = 3 ✓.