Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

maggieL

Find a such that th subspace-SPAN{(a, 1, 1), (0, 1, 2), (1, -1, 0)} of R^3 has dimension 2.

  • 9 months ago
  • 9 months ago

  • This Question is Open
  1. alexandercpark
    Best Response
    You've already chosen the best response.
    Medals 0

    i believe you just use some way to solve a system of equations (i would use RREF) and find a value of a such that one of those will zero out

    • 9 months ago
  2. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    I tried but couldn't get the zeros:(

    • 9 months ago
  3. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1372827825197:dw|

    • 9 months ago
  4. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    if the column space has dim( 2) the rank of matrice must be 2 and the null space must have dim 1 then a=-1/2

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

    um I'm trying to digest this... I'm actually a bit confused with the "null space". so does dimension2 mean 2 leading 1s with 1 free variable or am i just mixing things up?

    • 9 months ago
  6. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    Dim(R(A)=C(A'))=Dim(C(A))=rank A is mxn Dim(C(A))+dim(N(A'))=m Dim(R(A))+dim(N(A))=n dim(N(A))=n-r (number of free variables)

    • 9 months ago
  7. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    dimension is the number of vectors in a basis

    • 9 months ago
  8. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    the third column is the linear combination of the first two ones

    • 9 months ago
  9. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    if a =-1/2, then the column space is spaned by(1,-1,0) and (0,1,2)

    • 9 months ago
  10. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    does that mean: if it has dimension 3, there can't be any zero rows?

    • 9 months ago
  11. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    in this case yes

    • 9 months ago
  12. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    so a would be -1?

    • 9 months ago
  13. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    if a =-1 then the dim(C(A))=3 and the nullspace contains only zero vector

    • 9 months ago
  14. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    C(A)=R³

    • 9 months ago
  15. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    so if it has dimension 3, I would have to write a=-1 with the column space spanned by (1, -1, 0) (0, 1, 2) (-1, 1, 1)? sry I'm so smart with this:(

    • 9 months ago
  16. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not*

    • 9 months ago
  17. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    yes

    • 9 months ago
  18. maggieL
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks so much! ur so patient:)

    • 9 months ago
  19. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 3

    you are welcome

    • 9 months ago
    • Attachments:

See more questions >>>

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.