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(c) If S, T are subsets of a vector space, is [ST] = [S] n [T]? (d) Is the span of the complement equal to the complement of the span?

(c) If S, T are subsets of a vector space, is [ST] = [S] n [T]? (d) Is the span of the complement equal to the complement of the span?

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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Please do part D and If the statement is true, you don't need to prove it.  If the statement is not true, give a counterexample

2.48 Because 'span of' is an operation on sets we naturally consider how it interacts with the usual set operations. (a) If S CT are subsets of a vector space, is [S] [T]? Always? Sometimes? Never? (b) If S, T are subsets of a vector space, is [SUT] = [S] U [T]? tion I. Definition of Vector Space (c) If S, T are subsets of a vector space, is [SnT] = [S] n [T]? (d) Is the span of the complement equal to the complement of the span? 107
Transcribed Image Text:2.48 Because 'span of' is an operation on sets we naturally consider how it interacts with the usual set operations. (a) If S CT are subsets of a vector space, is [S] [T]? Always? Sometimes? Never? (b) If S, T are subsets of a vector space, is [SUT] = [S] U [T]? tion I. Definition of Vector Space (c) If S, T are subsets of a vector space, is [SnT] = [S] n [T]? (d) Is the span of the complement equal to the complement of the span? 107
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