A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 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 :(

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No problem! You're welcome

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.