(a) Every vector of R² is a linear combination of the vectors (-2,3),(1, 1) and (4,1)?(b) Is every vector in R³a linear combination of the vectors (-2, 1, 3) and (3, 2, 1)?(c) The Vector (2, –1,2) belong to the subspace generated by vectors (3,2, -1) and(-3,0,2}?

This is a question of linear algebra.

Answered: (a) Every vector of R² is a linear…

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 41CR: 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...

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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.
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(a) Every vector of R² is a linear combination of the vectors (-2,3), (1, 1) and (4,1)? (b) Is every vector in IR³ linear combination of the vectors (-2, 1, 3) and (3, 2, 1)? (c) The Vector (2, –1, 2) belong to the subspace generated by vectors (3,2, -1) and (-3,0,2}?