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maggieL Group Title

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

  • one year ago
  • one year ago

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  1. alexandercpark Group Title
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    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

    • one year ago
  2. maggieL Group Title
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    I tried but couldn't get the zeros:(

    • one year ago
  3. RaphaelFilgueiras Group Title
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    |dw:1372827825197:dw|

    • one year ago
  4. RaphaelFilgueiras Group Title
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    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

    • one year ago
  5. maggieL Group Title
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    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?

    • one year ago
  6. RaphaelFilgueiras Group Title
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    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)

    • one year ago
  7. RaphaelFilgueiras Group Title
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    dimension is the number of vectors in a basis

    • one year ago
  8. RaphaelFilgueiras Group Title
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    the third column is the linear combination of the first two ones

    • one year ago
  9. RaphaelFilgueiras Group Title
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    if a =-1/2, then the column space is spaned by(1,-1,0) and (0,1,2)

    • one year ago
  10. maggieL Group Title
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    does that mean: if it has dimension 3, there can't be any zero rows?

    • one year ago
  11. RaphaelFilgueiras Group Title
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    in this case yes

    • one year ago
  12. maggieL Group Title
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    so a would be -1?

    • one year ago
  13. RaphaelFilgueiras Group Title
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    if a =-1 then the dim(C(A))=3 and the nullspace contains only zero vector

    • one year ago
  14. RaphaelFilgueiras Group Title
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    C(A)=R³

    • one year ago
  15. maggieL Group Title
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    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:(

    • one year ago
  16. maggieL Group Title
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    I'm not*

    • one year ago
  17. RaphaelFilgueiras Group Title
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    yes

    • one year ago
  18. maggieL Group Title
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    thanks so much! ur so patient:)

    • one year ago
  19. RaphaelFilgueiras Group Title
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    you are welcome

    • one year ago
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