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Questions about rank and eigenvalues of a matrix

Let $$A=\begin{pmatrix}1&w&w^2\\w&w^2&1\\w^2&w&1\end{pmatrix}$$ Where $w$ is a complex no. s.t. $w^3=1$. Its clear by adding columns of matrix that $0$ is an eigen value of $A$.

Do there exist linearly independent vectors $u,v\in\mathbb{C}^3$ s.t. $Au=Av=0$?

can anyone help me please....

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    You may learn how to type mathematical formulae [here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference). It is a basic etiquette to format your question in a readable form.2012-12-17
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    Also, if you read a post and want to see how a mathematical expression in it was typed, you may right-click on it and choose "Show Math As > TeX Commands" from the context menu.2012-12-17
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    So you want to find the rank of A? What do eigenvalues have to do with it?2012-12-17
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    I want to find if there exist linearly independent vectors u,v∈C3 s.t. Au=Av=0?2012-12-17

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