Let u = [1, 2, 3, -1, 2]T, v = [2, 4, 7, 2, -1]T in ℝ5.
Find a basis of a space W such that w ⊥ u and w ⊥ v for all w ∈ W.
I think the question is quite easy. Given this vector w in the space W is orthogonal to both u and v. I can only think of w being a zero vector. But would this be too...