"In $\mathbb{P}_2$, find the change-of-coordinate matrix from the basis $B=\{1-3t^2, 2+t-5t^2, 1+2t\}$ to the standard basis. Then write $t^2$ as a linear combination of the polynomials in $B$."
I believe the CoC matrix to be: $\left(\begin{array}{ccc}1 &2& 1\\ 0& 1& 2\\ -3 &-5& 0\end{array}\right)$? Can someone confirm this? I also do not understand the second part of the question.