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Finding the dimension of the vector space spanned by 3 vectors

29-04-2010 10:14PM

#1

cian1500ww

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Anyone know of any good tutorials or guides on finding the dimension of a vector space spanned by 3 vectors ?? Haven't a clue how to approach it

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#2 29-04-2010 10:54PM

Fremen

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Mind posting up the specific problem?

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#3 29-04-2010 10:55PM

cian1500ww

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Fremen wrote: »

Mind posting up the specific problem?

Sure:
Consider the set of vectors V = fv1 = (1; 2; 1; 2); v2 = (1; 1; 1; 1); v3 =
(0; 0; 0; 1); v4 = (0; 1; 2; 0)g.
(i) What is the dimension of the vector space spanned by the vectors in V ?

It's for a maths assignment so I'm not looking for the answer (unfortunately :rolleyes:) Just how to solve it basically. Thanks !!

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#4 29-04-2010 11:00PM

Clinker

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Gaussian elimination will produce a linearly independent set with the same span.

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#5 29-04-2010 11:08PM

Fremen

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Yup, use Gaussian elimination to make as many zero rows as possible. Once you're done, the number of non-zero rows is the dimension of the subspace.

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#6 30-04-2010 12:57PM

cian1500ww

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Thanks for the help guys, much appreciated

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