8. Let W denote the subspace of R consisting of all the vectors havingcoordinates that sum to zero. The vectorsU1- (2, —3, 4, —5, 2), из 3D (-6,9, —12, 15, —6),из %3D (3, —2,7, —9, 1), ид 3Dus — (-1,1,2, 1, -3), ив 3Dи7 %3D (1,0, —2,3, —2), из %3D(2,–8, 2, –2, 6),(0, –3, –18, 9, 12),(2, –1,1, –9, 7)generate W. Find a subset of the set {u1, u2, . . . , u8} that is a basis forW.

Consider the provided question, Write the given vectors into a matrix as below,

Answered: 8. Let W denote the subspace of R…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
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