Q: In ℝ², find the dual basis to {(1,1),(1,-1)}. Evaluate e¹ on (3,1). Dual: e¹(v₁) = 1, e¹(v₂) = 0; e²(v₁) = 0, e²(v₂) = 1. Solve: e¹(x,y) = (x+y)/2: check: e¹(1,1) = 1 ✓, e¹(1,-1) = 0 ✓! e²(x,y) = (x-y)/2 ✓. e¹(3,1) = 2! (Dual basis: coordinate extractors!)