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1. Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span{u, v}.

1. Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span{u, v}.

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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1. Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span{u, v}. 2. Let H and K be subspaces of a vector space V. The intersection of H and K, denoted by HnK, is the set of v in V such that v belongs to both H and K. Show that HNK is a subspace of V.
Transcribed Image Text:1. Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u and v. Explain why H also contains Span{u, v}. 2. Let H and K be subspaces of a vector space V. The intersection of H and K, denoted by HnK, is the set of v in V such that v belongs to both H and K. Show that HNK is a subspace of V.
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