Kernel and image (rank-nullity theorem)
General · Mathematics
Study notes
Q: T: ℝ³→ℝ², T(x,y,z) = (x+y, z). Find rank and nullity. Kernel: x+y = 0, z = 0: {(-t,t,0)}: dim 1: nullity 1! Image: (a,b): x+y = a, z = b: all ℝ²: rank 2! Rank-nullity: 2+1 = 3 = dim ℝ³ ✓! (Surjective, not injective!)