Let $\displaystyle W=\{(x,y,z): x-y+2z=0\}$. Find the basis of $\displaystyle W$. Please help me in solving it.
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Do you know what the dimension of $\displaystyle W$ is?
big hint: z = (1/2)(y - x), so any vector of the form (x,y,(y-x)/2) is in W.
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