Answered: Determine whether the set of vectors is…

Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span. a. {[-1, 3, 1], [2, 1, 4]} in R^3 b. {[2, 1, -3], [4, 0, 2], (2, -1, 3]} in R^3?

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 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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Question

Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.

a. {[-1, 3, 1], [2, 1, 4]} in R^3

b. {[2, 1, -3], [4, 0, 2], (2, -1, 3]} in R^3?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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