The vector space $P_2(\mathbb{R})$ has a basis of $(P_1(x),P_2(x),P_3(x))$ and the polynomials $Q_1(x)=3+2x+7x^2, Q_2(x)=2+x+4x^2, Q_3(x)=5+2x^2$ with respect to this basis have the coordinates $(1,-2,0), \, (1,-1,0)$ and $(0,1,1)$.
Determine the three basis vectors $P_1(x), P_2(x)$ and $P_3(x)$.
How do I determine this? I have tried setting up a change of basis matrix $Q_1, Q_2, Q_3$ as columns and then calculated the matrix vector product with each coordinate, but it wasn't correct. Not sure what to do now.