Subspaces and quotient spaces
General · Mathematics
Study notes
Q: Is W = {(x,y,0)} a subspace of ℝ³? Describe ℝ³/W. Closed +, scalar ×: SUBSPACE (xy-plane!)! ℝ³/W: cosets (x,y,z)+W: determined by z! (a,b,c)+W = (0,0,c)+W: ≅ ℝ (z-coordinate!)! dim: 3-2 = 1 ✓! (Collapsing the plane to a point!)