My Math Forum Basis for Null Space of A, given a set of conditions
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 May 26th, 2009, 07:24 PM #1 Newbie   Joined: Apr 2009 Posts: 7 Thanks: 0 Basis for Null Space of A, given a set of conditions Let B = {v, w, x, y} be a basis for $R^4$, and let A be a 3x4 matrix with the following properties. Av = 0 vector A(v + 2y) = 0 vector Aw = $\left[ \begin{array}{ c c } 1 \\ 1\\ 1\end{array} \right]$ Ax = $\left[ \begin{array}{ c c } 0 \\ -1\\ -4\end{array} \right]$ 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.
 May 26th, 2009, 07:48 PM #2 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 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.
 May 26th, 2009, 08:21 PM #3 Newbie   Joined: Apr 2009 Posts: 7 Thanks: 0 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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