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Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3. v1 = (1, -1, 0) and v2 = (3, 1, -2)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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Question

Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3.

v1 = (1, -1, 0) and v2 = (3, 1, -2)

I've tried this, but I found that e1, e2, and e3 form det = 0. Is it right that e1, e2, e3 meet all the requirements?

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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