For the subspace W = {[x, y, z] ∈ R³ ∶ 2x − 2y + z = 0} of R³,

Question

find a basis for the orthogonal complement W‘ and verify that dim(W) + dim(𝑊') = dim(R³ ) Decompose v = [1, 2, 3] into w1 + w2, where 𝑤1 ∈ W and 𝑤2∈ 𝑊'

Answer 1