I have the following

B:=[p_0,p_1,p_2] denote the natural ordered basis for P_2(R)

C:=[h_1,h_2,h_3] where h_1(x)=7x^2+2x+3; h_2(x)=4x^2+5x+7 and

h_3(x)=-9x^2+x+1

Construct the change of coordinate matrix A which converts C-coordinates to B-coordinates.

Now my first thought was the rows in C are given by the columns in B, however when going through the calculations to construct f_c, in a later calculation. Do i have to find an expression for p_0, p_1 and p_2 using the equations?

many thanks in advance.