I have B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1) and C=(1+x^2, 1+x+2x^2, 1+4x+5x^2+x^3, -2+2x-x^2+5x^3).

Also, p(x)=3-8x+2x^2-6x^3.

I need to find [p]subscriptB and [p]subscriptC. What is it?

I'm really confused by my notes and nothing seems to work.

I need to show that the change of basis matrix from C to B times [p]subB=[p]subC and it doesn't work. I know the change of basis matrices.

Any help greatly appreciated.