the answer that was provided was great help thank you, but i had a similar type of question to this once and i used the same method but was marked incorrectly.. it didnt state to compute the inverse and was marked wrong. is there another way of doing it? thanks in advance
Let $B := [p_0, p_1, p_2]$ denote the natural ordered basis for $P_2(\mathbb R)$, the vector space of real polynomial functions of degree less than or equal to $2$. Define $f_1, f_2, f_3\in P_2(\mathbb R)$ by $f_1(x) = 1 − x$, $f_2 = x − x^2$ and $f_3(x) = 1 + 2x + x^2$. Define $C := [f_1, f_2, f_3]$. Verify that $C$ is an ordered basis for $P_2(\mathbb R)$. Compute the change of coordinates matrix $A$ which converts $B$-coordinates to $C$-coordinates. Define $f \in P_2(\mathbb R)$ by $f(x) = 3 − 4x + 2x^2$. Compute $f_C$.