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 .