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Suposse that {V1, V2, ..., Vp} is a basis for a subspace W, and suppose that v = a1V1+@2V2++a,Vp. Show that this representation of v is unique respect to this basis, this is, if v = v = b1V1 + b2v2 + ...+ b,Vp, then a1 = b1, a2 = b2, ... , ap = bp. %3D

Suposse that {V1, V2, ..., Vp} is a basis for a subspace W, and suppose that v = a1V1+@2V2++a,Vp. Show that this representation of v is unique respect to this basis, this is, if v = v = b1V1 + b2v2 + ...+ b,Vp, then a1 = b1, a2 = b2, ... , ap = bp. %3D

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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Suposse that {V1, V2, . .. , Vp} is a basis for a subspace W, and suppose that v = a¡V1+ª2V2+•·+a,Vp. Show that this representation of v is unique respect to this basis, this is, if v = v = b¡V1 + b2V2 + +b,Vp, then a1 = b1, a2 = b2, ... , ap = bp- ..
Transcribed Image Text:Suposse that {V1, V2, . .. , Vp} is a basis for a subspace W, and suppose that v = a¡V1+ª2V2+•·+a,Vp. Show that this representation of v is unique respect to this basis, this is, if v = v = b¡V1 + b2V2 + +b,Vp, then a1 = b1, a2 = b2, ... , ap = bp- ..
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