4. Let B- (v, Va. Vn) be a basis of a vector space, V. a) Prove just ONE of the following: • If S- {u, ua, Um) pans V then m 2n. • If S- (ui. ua, .. Um) is linearly independent then m Sn. b) Use (a)...

4. Let B- (v, Va. Vn) be a basis of a vector space, V.<br>a) Prove just ONE of the following:<br>• If S- {u, ua, Um) pans V then m 2n.<br>• If S- (ui. ua, .. Um) is linearly independent then m Sn.<br>b) Use (a) to show that the definition of dimension of V is well defined:<br>That is, if B = {V1, Va, Va) and B (u1, u2, , um) are bases of V then m = n.<br>

Extracted text: 4. Let B- (v, Va. Vn) be a basis of a vector space, V. a) Prove just ONE of the following: • If S- {u, ua, Um) pans V then m 2n. • If S- (ui. ua, .. Um) is linearly independent then m Sn. b) Use (a) to show that the definition of dimension of V is well defined: That is, if B = {V1, Va, Va) and B (u1, u2, , um) are bases of V then m = n.

Jun 04, 2022

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4. Let B- (v, Va. Vn) be a basis of a vector space, V. a) Prove just ONE of the following: • If S- {u, ua, Um) pans V then m 2n. • If S- (ui. ua, .. Um) is linearly independent then m Sn. b) Use (a)...

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