In R4 let
u1 = (0, 0, 0, -3), u2 = (0, 2, 3, -3), u3 = (-2, -4, -3, -3).
You are asked to determine the dimension of the subspace of R4 spanned by u1, u2, u3, and whether the set {u1, u2, u3} can be extended to a basis for R4.
1. The set {u1, u2, u3} is linearly independent.
2. The dimension of the subspace span{u1, u2, u3} is
3. The number of vectors in any basis for R4 is
The set {u1, u2, u3} cannot be extended to a basis for R4.
The set {u1, u2, u3, w} is a basis for R4, where
w = Enter a vector
