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Finding a Matrix whose kernel is spanned by 2 vectors

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Find a matrix whose kernel is spanned by the two vectors u=(1,3,2) and v=(-2,0,4).


    2. Relevant equations



    3. The attempt at a solution
    Tried setting vectors as a matrix and rref'ing it, but didn't know where I was getting at, also tried using an augmented identity matrix with both vectors then realized I didn't know what I was doing.
     
  2. jcsd
  3. Jan 26, 2009 #2

    Dick

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    How about finding a vector w that's orthogonal to both u and v and making a matrix where all of the rows are w?
     
  4. Jan 26, 2009 #3
    k I think I got it...
    Given:
    u=[1,3,2]
    v=[-2,0,4]

    I put in the vector M(1)=[1,1,1]
    M:=<u|v|M(1)>
    and I get...
    [1,-2,1
    3,0,1
    2,4,1]

    I apply rref, and I get an identity matrix. Meaning that the above matrix is my answer, right?
     
  5. Jan 26, 2009 #4

    Dick

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    That doesn't work. M*u is (-3,5,14) isn't it? If u is in the kernel M*u is supposed to (0,0,0). I don't think you heard me. Find a vector w so that u.w=0 and v.w=0. Wouldn't it work if you make a matrix with all of the rows w?
     
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