## anonymous one year ago The set B={3+1x^2, 9+4x+3x^2, −35−12x−12x^2} is a basis for P_3. Find the coordinates of p(x)= −46−8x−16x^2 relative to this basis

1. anonymous

It looks like you need to find constants $$a,b,c$$ such that $a(3+x^2)+b(9+4x+3x^2)+c(-35-12x-12x^2)=-46-8x-16x^2$ correct?

2. anonymous

If that's the case, then the problem comes down to solving the following system of equations: $\begin{cases} 3a+9b-35c=-46&\text{constant terms}\\ 4b-12c=-8&\text{linear terms}\\ a+3b-12c=-16&\text{quadratic terms} \end{cases}$

3. anonymous

@SithsAndGiggles thank you for looking, i tried solving the system and I got a = 236, b = 274, and c = 92, this was not correct :(

4. anonymous

How did you work through it? I used a calculator, and indeed that is not the right answer.

5. anonymous

@SithsAndGiggles i had -46 instead of -16 for the rhs of the last term, im getting the correct answer now, thank you :)!

6. anonymous

No problem! You're welcome