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Linear Algebra

Codexmax
in Linear Algebra and Group Theory

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Hey all!

I have tried to solve this problem and know part of it is right, i'd appreciate it very much if you could take a look at it.

 

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 so far that the kernel is the set {(r, -r, 0)}.

The range is R2.

What is the basis? And is the range right?

Thanks for your help!!!

Yes you're right about the Kernel and Range (are you required to write proofs for that or just give the answer?)

 

I'm fairly sure the basis is just the standard basis for R2, but don't hold me to that.

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