Let
be a
field,
and let
be a
-vector space.
Let
,
,
be a family of vectors in
, and let
be another vector. Assume that the family
-
is a system of generators of
, and that
is a linear combination of the
,
.
Prove that also
,
,
is a system of generators of
![{\displaystyle {}V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e613187d2bed7987812e6925fbbbedc048191f)
.