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).
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:
Thus, a=-6, b=8, c=-10, d=11.
So I said that [p]subscriptB is the vector:
, but this is obviously not right.
Any help or guidance would be greatly appreciated.
Why is this obviously not right? It looks OK to me.
Originally Posted by PvtBillPilgrim