Question: Let W V be a subspace. (a) Prove that dim W < dim V. (b) Prove that if dim W = dim V =

Let W ⊂ V be a subspace.
(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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