Give an example of each, or say why no example exists.
1) A Euclidean transformation that is not affine
2) An affine transformation that is not Euclidean
3) A transformation that is both Euclidean and affine
4) A transformation that is 1-1, but not Euclidean nor affine
1) This does not exist since ever Euclidean transformation of R^2 is an affine trans. since all orthogonal matrices are invertible
2) I know one exists, but am having trouble coming up with one. Do I just make the matrix A not be orthogonal, but still be invertible?
3) Here we can just take any Euclidean transformation since it will automatically be affine. So I can just give an such?
4) I am not sure here...do I just take the matrix to be any non-orthogonal, non-invertible matrix?
NEVER MIND, got it!