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Linear algebra - rank

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the rank of A =
    {[1 0 2 0]
    [4 0 3 0]
    [5 0 -1 0]
    [2 -3 1 1]}

    2. Relevant equations



    3. The attempt at a solution
    i row reduced A to be:
    {[1 0 0 0]
    [0 1 0 -1/3]
    [0 0 1 0]}

    where do i go from here?
     
  2. jcsd
  3. Oct 29, 2009 #2

    Dick

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    I think you omitted a last row of zeros. Ok, what does rank mean?
     
  4. Oct 30, 2009 #3
    The column rank of a matrix A is the maximal number of linearly independent columns of A. Likewise, the row rank is the maximal number of linearly independent rows of A.

    Since the column rank and the row rank are always equal, they are simply called the rank of A.
     
  5. Oct 30, 2009 #4

    Dick

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    Good! So how many linearly independent rows are there? If you have no idea, quote the definition of linear independence.
     
  6. Oct 30, 2009 #5
    so is it 3? because the 2nd and 4th columns are dependent.
     
  7. Oct 30, 2009 #6

    Dick

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    Yes, the second and fourth columns being dependent means the rank is at most 3. Now you have to check that the three remaining vectors are linearly independent. It's easier to see this if you look at the row reduction.
     
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