THEOREM 4.2.6 If S = {V1, V2, ..., vr} and S' = {W₁, W2, ..., Wk) are nonempty setsof vectors in a vector space V, thenspan{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 inS' is a linear combination of those in S. 22. Let v₁ = (1, 6, 4), v₂ = (2, 4, -1), V3 = (-1, 2, 5), andW₁ = (1, -2,-5), W₂ = (0, 8, 9). Use Theorem 4.2.6 to showthat span{V₁, V2, V3} = span{w₁, W₂}.

Given vectors are Here observed that So we have each of .In other words ,

Answered: 22. Let v₁ = (1, 6, 4), v₂ = (2, 4,…

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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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}.