# How to tell if a vector is in a subspace

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## 8 Replies - 11686 Views - Last Post: 06 June 2010 - 10:44 AM

### #1 NeoTifa

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# How to tell if a vector is in a subspace

Posted 02 June 2010 - 10:24 AM

How can you determine whether or not a vector is in a subspace created by a number of other vectors? I'm so confused! The book doesn't tell me anything useful. ;___;

A specific question I'm working on is v1 = (1, -2, 4, 3), v2 = (4, -7, 9, 7), v3 = (5, -8, 6, 5), and u = (-4, 10, -7, -5). Determine if u is in the subspace of R4 generated by {v1, v2, v3}

This post has been edited by NeoTifa: 02 June 2010 - 10:25 AM

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## Replies To: How to tell if a vector is in a subspace

### #2 xTorvos

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## Re: How to tell if a vector is in a subspace

Posted 02 June 2010 - 10:27 AM

Can you find vector u using a linear combination of the other three vectors?

### #3 xTorvos

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## Re: How to tell if a vector is in a subspace

Posted 02 June 2010 - 10:41 AM

I've worked out the answer to the question. Let me know when you'd like the solution.

### #4 NeoTifa

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## Re: How to tell if a vector is in a subspace

Posted 02 June 2010 - 12:42 PM

Bah, like an hour ago. I think I was gone the day he went over it and my book sucks. Just tell me how you did it, because I'm gonna have to turn in my blank homework

### #5 xTorvos

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## Re: How to tell if a vector is in a subspace

Posted 02 June 2010 - 02:35 PM

Sorry Neo, I forgot to check the reply!

Put the original vectors in an augmented matrix with u on the right side. When you get the augmented matrix in echelon form, you'll notice that you have 0's on the left side and non-zeros on the right. This shows that the set in inconsistent meaning that there is no linear combination of v1,v2,v3 that will get you u.

Again, sorry I didn't check back sooner.

### #6 NeoTifa

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## Re: How to tell if a vector is in a subspace

Posted 02 June 2010 - 04:34 PM

That's fine. Thanks, I had my prof explain it to me, and that's exactly what he said. ^__^ Finally, someone answered one of my homework questions!

### #7 xTorvos

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## Re: How to tell if a vector is in a subspace

Posted 03 June 2010 - 09:09 AM

You're welcome!

I'm just glad I could put my Linear Algebra skills to use. Just so you know, there are some great explanations of some of the LA concepts on youtube. The best ones I found were from a guy explaining on his computer using some software that makes his screen a blackboard. I can't get a link now because I'm at work but if you search for "linear algebra: introduction" you'll find them.

### #8 NeoTifa

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## Re: How to tell if a vector is in a subspace

Posted 03 June 2010 - 10:14 AM

Thanks. That could really help, especially since my final is monday :x

### #9 WSL

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## Re: How to tell if a vector is in a subspace

Posted 06 June 2010 - 10:44 AM