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Linear algebra: augmented matrix of a consistent system

  1. Aug 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the values of h such that the matrix is the augmented matrix of a consistent linear system.
    [1 h -5]
    [2 -8 6]

    2. Relevant equations

    None that I know of.

    3. The attempt at a solution

    Multiplied row (1) by -2:
    [-2 -2h 10 ]
    [ 2 -8 6 ]

    and added together to get: -2h -8 = 16
    and of course you can solve that for -2h=24
    and h = -12.

    So is it correct to say H can be any value other than -12 in order to make the system consistent? Please let me know if its correct. If not, please tell me what I need to do to get the correct answer. Thanks!
  2. jcsd
  3. Aug 27, 2011 #2


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    [-2 -2h 10 ]
    [ 2 -8 6 ]

    If you add together row 1 and 2 you will get

    [-2 -2h 10]
    [0 (-2h-8) 16]

    so yes -2h-8= 16 is one equation but will your matrix still be consistent if -2h-8 = 0?
  4. Aug 27, 2011 #3


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    Also, remember the matrix consists of only the coefficients of the equations. That second line corresponds to the equation (-2h-8)y = 16.

    What does it mean when a system is said to be consistent? How can that idea be related to that second equation?
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