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May 26th, 2009, 07:24 PM   #1
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Basis for Null Space of A, given a set of conditions

Let B = {v, w, x, y} be a basis for , and let A be a 3x4 matrix with the following properties.
Av = 0 vector
A(v + 2y) = 0 vector
Aw =
Ax =

Give a basis for the null space of A.

Sorry, one more problem. I tried doing this, but ended up getting the answer wrong, I was wondering how you would go about doing this particular problem?

Thanks so much.
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May 26th, 2009, 07:48 PM   #2
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Re: Basis for Null Space of A, given a set of conditions

A(v + 2y) = Av + 2Ay = 0

Hence Ay = 0.

I'll leave to you to show that no nontrivial linear combination of w, x will be mapped to the 0 vector.
A basis will be given by v,y.
brunojo is offline  
May 26th, 2009, 08:21 PM   #3
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Re: Basis for Null Space of A, given a set of conditions

ah. ok. I see now. I was approaching this problem in completely the wrong way.
Thanks!
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