Prove that if V is a vector space and S = {v1,v2,…,,vp } is any given set of vectors in V, then Span(S) is a subspace of V. Hint: You need to show three things: a. that 0V ∈ Span(S) b. that Span(S) is closed under addition c. that Span(S) is closed under scalar multiplication

Prove that if V is a vector space and S = {v1,v2,…,,vp } is any given set of vectors in V, then Span(S) is a subspace of V. Hint: You need to show three things: a. that 0V ∈ Span(S) b. that Span(S) is closed under addition c. that Span(S) is closed under scalar multiplication

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Prove that if V is a vector space and S = {v1,v2,…,,vp } is any given set of
vectors in V, then Span(S) is a subspace of V.
Hint: You need to show three things:
a. that 0V ∈ Span(S)
b. that Span(S) is closed under addition
c. that Span(S) is closed under scalar multiplication.

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