Gaussian elimination help

Question:The spanning set

[(2,2,1), (4,1,0), (2,-1,-1), (2,0,1)]

of R3 is not independent.

Explain why, and identify a

maximal independent set among these vectors.

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I'm having trouble with this question and i was wondering if someone could help me out and show me what I have to do to answer this question.

Re: Gaussian elimination help

Quote:

Originally Posted by

**kashmoneyrecord** Question:The spanning set

[(2,2,1), (4,1,0), (2,-1,-1), (2,0,1)]

of R3 is not independent.

Explain why, and identify a

maximal independent set among these vectors.

-----------------------------------------------------

I'm having trouble with this question and i was wondering if someone could help me out and show me what I have to do to answer this question.

Well the dimension of is three, so any set of four vectors is going to have to be linearly dependent.

Let . Then notice that

,

, and

,

where are the standard basis vectors. So spans and hence must be linearly independent.

Re: Gaussian elimination help

yo bro is that suffiencient enough to answer the question or is there more to it? and what does maximal independent set mean?

Re: Gaussian elimination help

okay got it thanks a lot :)