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Problem 5 Let S₁ and S₂ be subsets of a vector space V. Prove the followings: (1) span (S₁) span(S₂). (2) span (S₁ S₂) span(S₁) span (S₂). Give an example in which span(S₁ S₂) and span (S₁) span (S₂) are equal and one in which they are unequal. (3) span (S₁ US₂2) = span (S₁) + span(S₂).

Problem 5 Let S₁ and S₂ be subsets of a vector space V. Prove the followings: (1) span (S₁) span(S₂). (2) span (S₁ S₂) span(S₁) span (S₂). Give an example in which span(S₁ S₂) and span (S₁) span (S₂) are equal and one in which they are unequal. (3) span (S₁ US₂2) = span (S₁) + span(S₂).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 5 Let S₁ and S₂ be subsets of a vector space V. Prove the followings: (1) span (S₁) span(S₂). (2) span (S₁ S₂) span (S₁) n span (S₂). Give an example in which span(S₁ S₂) and span (S₁) span (S₂) are equal and one in which they are unequal. (3) span (S₁ U S2₂) = span (S₁) + span(S₂).
Transcribed Image Text:Problem 5 Let S₁ and S₂ be subsets of a vector space V. Prove the followings: (1) span (S₁) span(S₂). (2) span (S₁ S₂) span (S₁) n span (S₂). Give an example in which span(S₁ S₂) and span (S₁) span (S₂) are equal and one in which they are unequal. (3) span (S₁ U S2₂) = span (S₁) + span(S₂).
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