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Linear independence?

  1. Jul 7, 2010 #1
    How do you know when a matrix (or equivocally a system of equations) is linearly independent? How do you know that it's linearly dependent?

    For example, given this matrix,

    [ 1 1 2 1]
    [-2 1 4 0]
    [ 0 3 2 2]

    How do we know if this matrix is linearly independent or dependent?

    Thanks! :)
  2. jcsd
  3. Jul 7, 2010 #2


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    It isn't a matrix that is linearly dependent or independent. You can ask whether its rows or columns are. In this case the columns must be dependent because there are 4 of them and the columns have 3 components. To check whether the rows are dependent you would do row reduction. If a row becomes all 0 the rows are dependent.
  4. Jul 7, 2010 #3
    What do you mean by "3 components"?
  5. Jul 8, 2010 #4


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    Each column is a 3d column vector. It has, count 'em, three components.
  6. Jul 8, 2010 #5
    Ahhh. And by "components" you mean rows?
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