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Matrix problem

  1. Sep 13, 2006 #1
    hello.
    please help!!!

    this is the problem:
    determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

    1 -3 -2
    5 h -7

    i tried replacing and scaling... but it seems there are always 2 variable in this.
    can you guys help me solve this problem?
     
  2. jcsd
  3. Sep 13, 2006 #2

    J77

    User Avatar

    Is that an augmented system:

    1x-3y=-2
    5x+hy=-7

    ???
     
  4. Sep 13, 2006 #3
    is that not?
     
  5. Sep 13, 2006 #4
    is the answer any number... because with everynumber, there is a different solution to x and y?... probably true?
     
  6. Sep 13, 2006 #5
    ohkay... i think i got the answer... h cannot be 15, because than it will be

    1 -3 -2
    0 0 3
    this show that it will be inconsistent...
     
  7. Sep 13, 2006 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, you've "lost a sign". The row reduction of
    [tex]\left[\begin{array}{ccc}1 & -3 & -2 \\ 5 & h & 7\end{array}\right][/tex]
    is
    [tex]\left[\begin{array}{ccc}1 & -3 & 2\\ 0 &h+ 15 & 3\end{array}\right][/tex]

    What must h be so that is inconsistent?
     
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