Question: 4. Let V C R be a subspace. Define VI = {u e R : u is orthogonal to V). In other words V! =

4. Let V C R" be a subspace. Define VI = {u e R" : u is orthogonal to V). In other words V! = {u e R" : for all v E V, u . v = 0). (a) (2 points) Show that V- is a subspace of R".(b) (3 points) Let v E R". Suppose p1, p2 E V and n1, n2 E V- are such that v = pitn = P2 + 12. Prove that p1 = p2 and n1 = n2. This question is asking you to prove the uniqueness claim in Definition 5.2.13. So may not simply quote that.(c) (3 points) Prove that (V-) = V.O O (d) (2 points) Let A = 0 Let C(A) denote the column space of A. Find a basis NO for C(A)+

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