Let \( B=\left(1, x-1, x^{2}, x-2 x^{2}+x^{3}\right) \) and \( C=\left(1, x, x^{2}, x^{3}\right) \) be bases for \( P_{3} \). Find a matrix \( A \) such that \( [q(x)]_{C}=A[q(x)]_{B} \) for all \( q(x) \in \mathcal{P}_{3} \). Give only the values of the following entries of \( A \) :
a11 \( = \) \( \square \) \( a 12= \) \( \square \) \( a 23= \) \( \square \) \( a 44= \) \( \square \)
