A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Why is the set {1, x, x^2} a basis for P_2 when a+bx+cx^2 = a(1)+b(x)+c(x^2)? I understand that the this set spans P_2, but how do we know it's linearly independent?

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

    Because no linear combinations of any two of those vectors will yield any of the others.

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

    So, 1, x, and x^2 are all vectors, and k(1)+k(x)=x^2 is not consistent? Same thing with combinations of vectors in the set? I have trouble getting over the fact the something is a vector when it's not expressed in the form (a,b,c) or whatever.

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

    other vectors in the set*

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

    The graph of k(1)+k(x) will never equal the graph of x^2. Therefore they are linearly independent.

  5. 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.