Codexmax

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!!!