## decomposing vectors

Linear spaces and subspaces, linear transformations, bases, etc.
MmaureenT
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Joined: Wed Sep 28, 2011 7:02 pm
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### decomposing vectors

In this thread, the instructions say to decompose:

. . . . .$\left\, =\, \left<-\frac{5}{3}r\, -\, \frac{8}{3}s\, -\, \frac{4}{3}t,\, r,\, s,\, t\right>$

Now decompose this into three vectors multiplied by r, s, and t, and I believe you'll have your basis vectors.

I'm not sure what you mean by decompose. If you multiplied it out I don't see how it gives an answer. I think I have a similar problem that can be solved this way, but I don't understand what I'm supposed to do next :(

maggiemagnet
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Joined: Mon Dec 08, 2008 12:32 am
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### Re: decomposing vectors

MmaureenT wrote:I'm not sure what you mean by decompose. If you multiplied it out I don't see how it gives an answer.

It already is "multiplied out". What you need to do now is take it apart ("decompose" it) into the three vectors which were added to get this vector, and then factor "r" out of the vector with just "r" terms, "s" out of the vector with just "s" terms, and "t" out of the vector with just "t" terms.