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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,).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Start with finding TWO vectors u and v of R' which are linearly independent (you can see this i. 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 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;).
Transcribed Image Text:Start with finding TWO vectors u and v of R' which are linearly independent (you can see this i. 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 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;).
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