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
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=(1,0,1,1), 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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