### Can I get coefficients of a vector with respect to given basis for a vector space.

Hello.

I have a question.

For example,

- make vector space
`V`

by a basis `B=[1+x,3*x,x^2]`

over the field of rationals`Q`

`v=3*x^2+17*x+5`

in V `v=a*B[0]+b*B[1]+c*B[2]`

for some `a,b,c`

in `Q`

`[a,b,c]`

=?

We easily know the solution of previous example.

In general, for given basis `B`

and a vector `v`

, how can I get the list of coefficients?

And is it possible to the case of matrix space (`B`

: the basis consists of matrices) ?

Thanks. :)