Find a basis for the subspace of R4 spanned by the given vectors. (1,1,-6,-7), (2,0,2,-2), (3,-1,1,27) O (1,0,0,0) and (0,0,1,0) O (1,1,-6,-7) O (1,1-6,-7), (0,1,-7-6), and (0,0,1,-8/3) O (1,1-6,-7) (0,1,0,0) O (1,0,0,0), (0,1,0,0), and (0,0,1,0)
Find a basis for the subspace of R4 spanned by the given vectors. (1,1,-6,-7), (2,0,2,-2), (3,-1,1,27) O (1,0,0,0) and (0,0,1,0) O (1,1,-6,-7) O (1,1-6,-7), (0,1,-7-6), and (0,0,1,-8/3) O (1,1-6,-7) (0,1,0,0) O (1,0,0,0), (0,1,0,0), and (0,0,1,0)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 42EQ
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Transcribed Image Text:Find a basis for the subspace of R4 spanned by the given vectors.
(1,1-6,-7), (2,0,2,2), (3,-1,1,27)
O (1,0,0,0) and (0,0,1,0)
O (1,1,-6,-7)
O (1,1-6,-7), (0,1,-7,-6), and (0,0,1,-8/3)
O (1,1-6,-7) (0,1,0,0)
O (1,0,0,0), (0,1,0,0), and (0,0,1,0)
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 = (5,-6,14,6), v4 = (0,4,2,-3), v5 = (-10,53,45,-19)
O v1. V2, V5 form the basis; v3 = 4v1+V2, V4 = 4v1 + 7v2
V1, V2, V4 form the basis; v3 = 3v1+V2, V5 = 4v1+ 9v2 + 7v4
O v1. V2, V4 form the basis; v3 = 3v1- V2. V5 = 4v1 + 7v2+ 9v4
Vị forms the basis; v2 = - 3v1, V3 = 3v1, V4 = - 7V1, V5 = 4v1
O v1. V2, V3 form the basis; v4 = 3v1- V2, V5 = 4v1 + 7v2+ 9v3
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