Answer to Question #338744 in Linear Algebra for Mpho

Question

Consider the vector space V = C

2 with scalar multiplication over the real numbers R and let W

and U be the subspaces of V defined by

W = {(z1, z2) ∈ V : z2 = z1 + 2z1} and U = {(z1, z2) ∈ V : z2 = z1 − z1}.

2.1 Find a basis for W ∩ U.

2.2 Express (z1, z2) ∈ V as (z1, z2) = w + u where w ∈ W and u ∈ U.

2.3 Explain whether V = W ⊕ U

Answer 1

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