# If X is any set of vectors in an inner product space V, define X = {v | v in V, (v, x) = 0 for all x in X}. (a) Show that X is a subspace of V. (b)

If X is any set of vectors in an inner product space V, define

X⊥ = {v | v in V, (v, x) = 0 for all x in X}.

(a) Show that X⊥ is a subspace of V.

(b) If U = span, (u1,u2..., um}, show that (U⊥ = {u1,...,um.

(c) If X⊂ Y, show that Y⊥ ⊂ X⊥.

(d) Show that X⊥ ∩ Y⊥ = (X ∪ Y) ⊥

X⊥ = {v | v in V, (v, x) = 0 for all x in X}.

(a) Show that X⊥ is a subspace of V.

(b) If U = span, (u1,u2..., um}, show that (U⊥ = {u1,...,um.

(c) If X⊂ Y, show that Y⊥ ⊂ X⊥.

(d) Show that X⊥ ∩ Y⊥ = (X ∪ Y) ⊥

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## b If v is in U then v u 0 for all u in U In particular v ui 0 for 1 i …View the full answer

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