Let
be a
basis
of a three-dimensional
-vector space
.
a) Show that
is also a basis of
.
b) Determine the
transformation matrix
.
c) Determine the transformation matrix
.
d) Compute the coordinates with respect to the basis
for the vector, which has the coordinates
with respect to the basis
.
e) Compute the coordinates with respect to the basis
![{\displaystyle {}{\mathfrak {w}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17817534496a744d36ead0f08241c66070b09982)
for the vector, which has the coordinates
![{\displaystyle {}{\begin{pmatrix}3\\-7\\5\end{pmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d14c607111202e72a7bc2b0ba2d3f47819020eca)
with respect to the basis
![{\displaystyle {}{\mathfrak {v}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/141620e29cf8517dee128b1cf63c7226b9d95872)
.