I have a set
$S = \{ x^2 + 1, x + 1, 1 - x, x^3 \}$
in a polynomial vector space.
How do I write a vector matrix of $S$ in the base $B = \{ 1, x, x^2, x^3 \}$?
I attempted this using the formula: $M(S) = B^{-1} * T * B$, where $T$ is the matrix of the set.
I got the following result:
$ T=\left(\begin{matrix} 1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1 \end{matrix}\right) $ Is this correct or have I missed something?
I don't have the solutions so I cannot confirm it.