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Question: 11 please...

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10: Prove th e Dimension Theorem for Orthogonal Complements: If W is a subspace of R with orthogonal complement Wi, then dim(W) Proof: Let B-(te i, ti, . . . , uhS Rn be a basis of W. Then w = span(B). + dim(W+) = n. Construct a matrix A = W-Span(B)-rowspace(A) and Wi=nullspace(A) → Therefore, dim(W) + dim(Ww) - dimrouspace(A) + dim(nullspace(A) rank(A) + nullity(A) number of columns =n Wnw0). plement W. Prove that 11: Let W be a subspace of R with orthogonal com Proof 11 please
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