Affine mapping/Basis/Image points/Mapping properties/Exercise

Let and be affine spaces over the field , let be an affine basis of , and let denote points. Let

be the corresponding affine-linear mapping with

Show the following statements.

a) is bijective if and only if is an affine basis of .


b) is injective if and only if are affinely independent.


c) is surjective if and only if is an affine generating system of .