We consider the families of vectors
-
in
.
a) Show that
and
are both a
basis
of
.
b) Let
denote the point which has the coordinates
with respect to the basis
. What are the coordinates of this point with respect to the basis
?
c) Determine the
transformation matrix
which describes the
change of bases
from
![{\displaystyle {}{\mathfrak {v}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/141620e29cf8517dee128b1cf63c7226b9d95872)
to
![{\displaystyle {}{\mathfrak {u}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c827f23d0b620bf091abcb9422b4e1136c3c0a1d)
.