find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Linear spaces and subspaces, linear transformations, bases, etc.
lawrence
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find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby lawrence » Tue May 19, 2009 4:58 pm

Find a basis for the set of all vectors of the form (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c).

This made so much sense in the book. :oops:

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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby Matt » Tue May 19, 2009 9:47 pm


lawrence
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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby lawrence » Fri May 22, 2009 5:00 pm

So the basis is just ? It's that easy? :oops:

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Martingale
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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby Martingale » Sat May 23, 2009 3:17 am

lawrence wrote:So the basis is just ? It's that easy? :oops:



No...that is not the answer

lawrence
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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby lawrence » Sat May 23, 2009 2:11 pm

Could you give me another hint, please?

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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby Martingale » Sat May 23, 2009 2:14 pm




therefore the vectors are not linearly independent

lawrence
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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby lawrence » Sat May 23, 2009 3:36 pm

So this is where I have to do the vector-sum equals zero thing? When I solve the matrix, I get...



So a=-c, b=2c. If c=-1, then a=1,b=-2 and (1,2,-1,3)+(4,-10,8,-2)+(-5,8,-7,-1) = (0,0,0,0). So the answer is just the first two vectors, (1,2,-1,3),(-2,5,-4,1)?

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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby Martingale » Sat May 23, 2009 3:58 pm

lawrence wrote:So this is where I have to do the vector-sum equals zero thing? When I solve the matrix, I get...



So a=-c, b=2c. If c=-1, then a=1,b=-2 and (1,2,-1,3)+(4,-10,8,-2)+(-5,8,-7,-1) = (0,0,0,0). So the answer is just the first two vectors, (1,2,-1,3),(-2,5,-4,1)?



those two vectors will work

lawrence
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Re: find basis for (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c)

Postby lawrence » Sun May 24, 2009 1:18 am

I don't know why I'm having so much trouble with this. Thank you for your help!


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