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Linear algebra, rank and nullity

  1. Apr 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the rank and nullity of the given matrix:

    |-2 2 1 1 -2 |----->(1)
    |1 -1 -1 -3 3 |----->(2)
    |-1 1 -1 7 5 |----->(3)


    The attempt at a solution
    i know rank is the number of non-zero rows and nullity is the # of columns minus the rank
    matrix:
    i took (1)+(2) then (1) x -1 to get:
    |1 -1 0 2 -1 |
    | 1 -1 -1 -3 3 |
    |-1 1 -1 7 5 |

    (2)+(3)

    |1 -1 0 2 -1 |
    |0 0 -2 4 8 |
    |-1 1 -1 7 5 |

    (3)+(1)
    |1 -1 0 2 -1 |
    |0 0 -2 4 8 |
    |0 0 -1 9 4 |

    by this the rank should be 3 right? and the nullity is 5-3 = 2

    the correct answer is rank 2 and nullity 3
    what am i doing wrong?
     
  2. jcsd
  3. Apr 20, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    You have probably made some calculation errors.

    For example, in your first step, instead of
    |1 -1 0 2 -1 |
    | 1 -1 -1 -3 3 |
    |-1 1 -1 7 5 |

    I get

    |1 -1 0 2 -1 |
    | 1 -1 0 2 -1|
    |-1 1 -1 7 5 |
     
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