Mathematics - Linear Algebra - Determinants - Computing Determinants

10 steps: (1) 2×2: det[[a,b],[c,d]] = ad-bc. (2) Example: det[[3,1],[2,5]] = 15-2 = 13. (3) Geometric meaning: absolute value = area scale factor. Sign = orientation. (4) det=0 means matrix is SINGULAR (not invertible, columns are linearly dependent). (5) 3×3: expansion along first row (cofactor exp