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Homework Help: Linear independent vectors

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Determine whether the vector v1=(!,2,3),v2(3,2,1) and v3(1,1,1) are independent or dependent.


    2. Relevant equations
    I'm so lost


    3. The attempt at a solution
    I'm so lost
     
  2. jcsd
  3. Apr 4, 2010 #2
    Re: Vectors

    Is that suppose to be ! or 1?

    If it is suppose to be a 1, just put it in a matrix and do reduced row echelon form. If you don't get back the identity matrix, they aren't independent.
     
  4. Apr 4, 2010 #3
    Re: Vectors

    I'm sorry that's suppose to be a 1
     
  5. Apr 4, 2010 #4
    Re: Vectors

    Ok, now just set up a 3 x 3 matrix and reduce the rows.
     
  6. Apr 4, 2010 #5
    Re: Vectors

    When I set up the matrix and reduce the rows. This will show if its independent or independent?
     
  7. Apr 4, 2010 #6

    Mark44

    Staff: Mentor

    Re: Vectors

    It will show whether the vectors are linearly independent or linearly dependent.
     
  8. Apr 4, 2010 #7
    Re: Vectors

    Yes, because if you don't obtain the identity matrix, one or two of the vectors are dependent.
    [1,0,5]
    [0,1,2]
    [0,0,0]
    Take this rref matrix as an example.
    This is telling us the 3rd column can be written as 5v1+2v2.
     
  9. Apr 4, 2010 #8
    Re: Vectors

    oh okay, thanks
     
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