Let W V be a subspace. (a) Prove that dim W < dim V. (b) Prove
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(a) Prove that dim W < dim V.
(b) Prove that if dim W = dim V = n < ∞, then W = V. Equivalently, if W ⊆ V is a proper subspace of a finite-dimensional vector space, then dim W < dim V.
(c) Give an example where the result is false if dim V = ∞.
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a If dimV then the inequality is trivial Also if dimW the...View the full answer
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