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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=(1,0,1,1), v2 = (-5,5,2-2), v3 = (-1,5,6,2), v4 = (-9,5,-2,-6) V1, V2, V4 form the basis; v3 = -4v1 + v2 + 2v4 V1. V2 form the basis; v3 = 4v1+ V2, V4 = -4v1 + V2 V2, V3, V4 form the basis; v1 = 5v2+ 2v3+ 3v4 O v1, V3, V4 form the basis; v2 = -1V1 + V3 + 7v4 O v1, V2, V3 form the basis; v4 = 4v1+ V2+ 3v3

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=(1,0,1,1), v2 = (-5,5,2-2), v3 = (-1,5,6,2), v4 = (-9,5,-2,-6) V1, V2, V4 form the basis; v3 = -4v1 + v2 + 2v4 V1. V2 form the basis; v3 = 4v1+ V2, V4 = -4v1 + V2 V2, V3, V4 form the basis; v1 = 5v2+ 2v3+ 3v4 O v1, V3, V4 form the basis; v2 = -1V1 + V3 + 7v4 O v1, V2, V3 form the basis; v4 = 4v1+ V2+ 3v3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 14E
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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=(1,0,1,1), v2 = (-5,5,2-2), v3 = (-1,5,6,2), v4 = (-9,5,-2,-6) V1, V2, V4 form the basis; v3 = -4v1 + v2 + 2v4 V1. V2 form the basis; v3 = 4v1+ V2, V4 = -4v1 + V2 v2, V3, V4 form the basis; v1 5v2+ 2v3+ 3v4 O v1, V3, V4 form the basis; v2 = -1v1 + V3 + 7v4 O v1, V2, V3 form the basis; v4 = 4v1+ V2 + 3v3
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=(1,0,1,1), v2 = (-5,5,2-2), v3 = (-1,5,6,2), v4 = (-9,5,-2,-6) V1, V2, V4 form the basis; v3 = -4v1 + v2 + 2v4 V1. V2 form the basis; v3 = 4v1+ V2, V4 = -4v1 + V2 v2, V3, V4 form the basis; v1 5v2+ 2v3+ 3v4 O v1, V3, V4 form the basis; v2 = -1v1 + V3 + 7v4 O v1, V2, V3 form the basis; v4 = 4v1+ V2 + 3v3
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