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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
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It looks like you need to find constants \(a,b,c\) such that \[a(3+x^2)+b(9+4x+3x^2)+c(3512x12x^2)=468x16x^2\] correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If that's the case, then the problem comes down to solving the following system of equations: \[\begin{cases} 3a+9b35c=46&\text{constant terms}\\ 4b12c=8&\text{linear terms}\\ a+3b12c=16&\text{quadratic terms} \end{cases}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles thank you for looking, i tried solving the system and I got a = 236, b = 274, and c = 92, this was not correct :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How did you work through it? I used a calculator, and indeed that is not the right answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles i had 46 instead of 16 for the rhs of the last term, im getting the correct answer now, thank you :)!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No problem! You're welcome
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