Start with finding TWO vectors u and v of R' which are linearly independent (you can see thisi.by checking that they are not scalar multiples of each other).ii.From the standard basis of R, we have the vectors e, = (1,0,0), e, = (0,1,0), and ez = (0,0,1).Deduce which of e,, ez, and e, that will make a linearly independent set together with u andv. Prove your claim. Only 1 set is needed (i.e. if e, works, then you don't have to test for e,and e;).

In the given question we have to find the the Linearly independent vectors in ℝ3. Concept: In a set…

i. Start with finding Two vectors u and v of R' which are linearly independent (you can see this by checking that they are not scalar multiples of each other). ii. From the standard basis of R', we have the vectors e, = (1,0,0), e; = (0,1,0), and e, = (0,0,1). Deduce which of e, e, and e, that will make a linearly independent set together with u and v. Prove your claim. Only 1 set is needed (i.e. if e, works, then you don't have to test for e, and e,).

i. Start with finding Two vectors u and v of R' which are linearly independent (you can see this by checking that they are not scalar multiples of each other). ii. From the standard basis of R', we have the vectors e, = (1,0,0), e; = (0,1,0), and e, = (0,0,1). Deduce which of e, e, and e, that will make a linearly independent set together with u and v. Prove your claim. Only 1 set is needed (i.e. if e, works, then you don't have to test for e, and e,).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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