Let S = {a,b,c}be a subset of a vector space V. Consider a new set M = {W₁, W₂, W3}, such that W₁ = a + b + c W₂ = a - b + c W3 = a-b-c Prove that span(S) = span(M)
Let S = {a,b,c}be a subset of a vector space V. Consider a new set M = {W₁, W₂, W3}, such that W₁ = a + b + c W₂ = a - b + c W3 = a-b-c Prove that span(S) = span(M)
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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![Let S = {a,b,c}be a subset of a vector space V.
Consider a new set M = {W₁, W₂, W3}, such that
W₁ = a + b + c
W₂ = a - b + c
W3 = a-b-c
Prove that span(S) = span(M)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98b6e310-08ba-4e1d-a9bc-704b45d2ce6c%2F30d9c435-dc51-43a8-aa2c-eb5353b96737%2Fp1fnik_processed.png&w=3840&q=75)
Transcribed Image Text:Let S = {a,b,c}be a subset of a vector space V.
Consider a new set M = {W₁, W₂, W3}, such that
W₁ = a + b + c
W₂ = a - b + c
W3 = a-b-c
Prove that span(S) = span(M)
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