basis for polynomials

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.

Basically, what's the equation/formula for [p]subscriptB?

Here's my work for finding [p]subscript B:
I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
I solved for a,b,c,d and got:
a=-6
b+a=2
a+b+c=-8
a+b+c+d=3

Thus, a=-6, b=8, c=-10, d=11.

So I said that [p]subscriptB is the vector:
[-6
8
-10
11]
, but this is obviously not right.

Any help or guidance would be greatly appreciated.

Quote:

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Originally Posted by PvtBillPilgrim

Basically, what's the equation/formula for [p]subscriptB?

Here's my work for finding [p]subscript B:
I have the equation p(x)=3-8x+2x^2-6x^3 and B=(1+x+x^2+x^3, 1+x+x^2, 1+x, 1).
I said a(1+x+x^2+x^3)+b(1+x+x^2)+c(1+x)+d=3-8x+2x^2-6x^3.
I solved for a,b,c,d and got:
a=-6
b+a=2
a+b+c=-8
a+b+c+d=3

Thus, a=-6, b=8, c=-10, d=11.

So I said that [p]subscriptB is the vector:
[-6
8
-10
11]
, but this is obviously not right.

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Why is this obviously not right? It looks OK to me.

RonL