Math Is Fun Forum

LorraineBR

Guest

Linear dependance and span

can anyone please tell me in really simple english how i could find if a group of vectors are linear dependant
e.g (0, 1), (0, -2);

also if you could maybe explain how to find out if vectors span IR3 or IR4
e.gDetermine whether the vectors span IR3:
          (ii) v1 = (1;-2; 0), v2 = (2;-1; 0), v3 = (3; 0; 0), v4 = (1; 0; 1).

thank you

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Linear dependance and span

since we have 2 2D vectors a quick and simple method to show they are linearly dependant is to check that

therefore they are linearly dependant

this method of using determinants of course only works if you have 'n' number of n'th dimensional vectors

Last edited by luca-deltodesco (2009-05-13 03:26:57)

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear dependance and span

Hi LorraineBR;

Also the second vector is -2 times the first vector. A sure sign of linear dependence.

Here is a page that I have used for these type of problems.
http://ltcconline.net/greenl/courses/203/Vectors/linIndSpan.htm

Last edited by bobbym (2009-05-13 03:43:21)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

LorraineBR

Guest

Re: Linear dependance and span

id like to thank both of you so much.
especially bobbymn your webpage is extreemely helpful

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Linear dependance and span

I'm glad you understand it. Don't want  to do anymore Linear Algebra. Nullspaces,vector spaces, basis vectors, spans, eigenvalues,eigenvectors ,Uhhhh.

Last edited by bobbym (2009-05-13 04:23:41)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.