Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁-(1,-1,5,2), V₂ = (-2,3,1,0), v3 = (4-5,9,4), v4 = (0,4,2,-3), vs = (-1,25,49,-1) OV1, V2. V4 form the basis; V3-2V1-V2, Vs=7V1+4V2+5V4 V₁ forms the basis; V2=-2V1, V3-2V1, V4=-4V1, VS = 7V1 V₁ V2 V4 form the basis; V3 2v1+V2 V5 = 7V1 +5V2 + 4V4 V1, V2, V3 form the basis; V4-2V1-V2, V5-7V1+4V2+5V3 V1, V2, V3 form the basis; V3-7V1+V2, V4-7V1 +42
Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as a linear combination of the basis vectors. V₁-(1,-1,5,2), V₂ = (-2,3,1,0), v3 = (4-5,9,4), v4 = (0,4,2,-3), vs = (-1,25,49,-1) OV1, V2. V4 form the basis; V3-2V1-V2, Vs=7V1+4V2+5V4 V₁ forms the basis; V2=-2V1, V3-2V1, V4=-4V1, VS = 7V1 V₁ V2 V4 form the basis; V3 2v1+V2 V5 = 7V1 +5V2 + 4V4 V1, V2, V3 form the basis; V4-2V1-V2, V5-7V1+4V2+5V3 V1, V2, V3 form the basis; V3-7V1+V2, V4-7V1 +42
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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Transcribed Image Text:Find a subset of the vectors that forms a basis for the space spanned by the vectors, then express each vector that is not in the basis as
a linear combination of the basis vectors.
V₁=(1,-1,5,2). V₂ = (-2,3,1,0), v3 = (4,-5,9,4), v4 = (0,4,2,-3), vs = (-1,25,49,-1)
V1, V2, V4 form the basis; V3 = 2v1 - V2. V5 = 7V1+4v2 +5V4
O v₁ forms the basis; V2=-2V1, V3 = 2v1. V4 = -4V1. V5 = 7V1
V1, V2, V4 form the basis; V3 = 2v1+V2, V5 = 7V1 +52 +44
V1, V2, V3 form the basis; V4 = 2V1 - V2. V5 = 7V1 + 4V2 + 5V3
V1, V2, V5 form the basis; V3 = 7V1+V2 V4 = 7V1 + 4V2
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