(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm working on change-of-basis matrices and vector spaces.

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.

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.

2. Relevant equations

Nothing relevant that I can think of. It's probably what I'm missing. What exactly is the equation/formula for [p]subscriptB and [p]subscriptC?

3. The attempt at a solution

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.

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# Algebra help

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