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I am working on this and got confused. Any help at all would be much appreciated!

Determine the kernel and range of the transformation T and find a basis for each: T(x,y,z)=(x,y,z) from R3 to R2.

I have found the kernel to be the set {(r, -r, 0)}.

Range is R2.

I"m not sure how to find the basis. Any ideas? I think the range is right but not sure.

Thanks guys!