> 
> Let W be the subspace spanned by the given vectors. Find a basis for $W^\perp$.
>  $$v\_1=(2,1,-2) ;v\_2=(4,0,1)$$
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Well I did the following to find the basis. 

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> $$(x,y,z)\*(2,1,-2)=0$$ $$(x,y,z)\*(4,0,1)=0$$
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If you simplify this in to a Linear equation

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> $$2x + y - 2z = 0$$ $$4x + z = 0$$
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Now bu placing this in a vector and performing row echelon I get

$$ w = 
\left[ \begin{array}{ccc|c}
1 &\ 0 &\ 1/4 &0\\ 
0&\ 1 &\ -5/2 &0
\end{array} \right]$$

By solving this I get

> 
> $$x=-1/4 t$$
>  $$y=5/2 t$$
>  $$z=t$$
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By this I get the basis to be.

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> $$[-1/4, 5/2 ,1]$$
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I don't see that the answer is correct because you get the vector space in the someway. Please tell me if I used the correct method.
Thank you