Basis and dimension
General · Mathematics
Study notes
Q: Is {(1,1),(1,-1)} a basis of ℝ²? Find coordinates of (3,1). Independent? a(1,1)+b(1,-1) = 0: a+b = 0, a-b = 0: a = b = 0 ✓. Spans ℝ² (2 indep in dim 2!) ✓: BASIS! (3,1) = a(1,1)+b(1,-1): a+b = 3, a-b = 1: a = 2, b = 1. Coordinates: (2,1)!