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22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use Theorem 4.2.6 to show that span{v₁, V2, V3} = span{w₁, W₂}.

22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), w₂= (0, 8, 9). Use Theorem 4.2.6 to show that span{v₁, V2, V3} = span{w₁, W₂}.

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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THEOREM 4.2.6 If S = {V1, V2, ..., vr} and S' = {W₁, W2, ..., Wk) are nonempty sets of vectors in a vector space V, then span{V1, V2, ..., vr} = span{w₁, W2, ..., Wk} if and only if each vector in S is a linear combination of those in S', and each vector in S' is a linear combination of those in S.
Transcribed Image Text:THEOREM 4.2.6 If S = {V1, V2, ..., vr} and S' = {W₁, W2, ..., Wk) are nonempty sets of vectors in a vector space V, then span{V1, V2, ..., vr} = span{w₁, W2, ..., Wk} if and only if each vector in S is a linear combination of those in S', and each vector in S' is a linear combination of those in S.
22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), W₂ = (0, 8, 9). Use Theorem 4.2.6 to show that span{V₁, V2, V3} = span{w₁, W₂}.
Transcribed Image Text:22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), and W₁ = (1, -2,-5), W₂ = (0, 8, 9). Use Theorem 4.2.6 to show that span{V₁, V2, V3} = span{w₁, W₂}.
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