A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

if a1=(7,-1,4) a2=(4,0,1) and a3=(-3,5,0) and the set S={a1,a2,a3} is a basis for R3, how do you find the equation y=2a1-3a2+a3 (ps that is the answer, I just don't know how to get to it)

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

    trying to find the linear combination y, they give the answer but they dont explain how they got to it

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

    perhaps I am reading this wrong

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

    do you know the coordinates of y?

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

    y=(-1,3,5)

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

    didnt think it was part of it, but they did mention that a little before

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

    yes, that is the important bit. a1(x,y,z) = (7,-1,4) a2(x,y,z) = (4,0,1) and a3(x,y,z) = (-3,5,0)

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

    right, so how do we find the linear combination?

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

    so a linear combination of the x-coordinates of a1,a2,a3 should give the x- coordinate of y, a linear combination of the y-coordinates of a1,a2,a3 should give the y- coordinate of y, a linear combination of the z-coordinates of a1,a2,a3 should give the z- coordinate of y.

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

    so 7m+4n-3p=-1 -m+5p=3 and4m+n = 5

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

    ahh ok thanks a lot, then solve the matrix from there eh?

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

    3 equations, 3 unknowns, solve to get m,n,p those will be the coefficients of the equation y = ma1+na2+pa3

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

    just one more thing....what did we do here? we had a coordinate, then we established the basis, and found another coordinate

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

    did we change it from cartesian?

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

    no its in Cartesian coordinates only. all we did was to find a linear combination of the three points which gives the point y.

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

    it follows that [y]s=(2,-3,1) in the text, this isn't a coordinate?

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

    no, those are the coefficients of the linear combination.

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

    i gotta run, hope that helped!

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

    thanks!

  19. 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.