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Math Help - Linear Applications dealing with Matricies

  1. #1
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    Linear Applications dealing with Matricies

    Find the relationship between a,b, and c for which the system of equations will be consistent.

    2x+y-z=a
    x+2y+z=b
    5x+4y-z=c

    I need help for this, i can't seem to get the answer that the book has in the back which is, 2a+b-c=0. Can someone plzz help me solve this, or show me step by step on how to do this. Thanks!!

    I know Jhevon gave me some help, but i can't seem to get that answer. Can someone actually show me step by step how to do it...
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  2. #2
    MHF Contributor
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    This is one of life's great dilemmas. No matter what answers you put in the back of the book, someone will find a way to misuse and abuse them. The author MUST put something, but it must be done with the greatest of fear.

    One does not want to create dependence.
    One cannot guarantee that all are exactly correct.

    It remains for the student to gain a little fortitude and discern for himself when an answer is incorrect.

    What do you know about "consistent" systems?

    If the right answer is 2a + b - c = 0, then pick some values and PROVE it. I tried a = b = 1 and c = 3. Guess what? No solution. The answer cannot be correct unless the question is written incorrectly.

    Solve the first for a variable: y = a + z - 2x
    Substitute into the other two:

    2a - 2x + 2z = b
    4a - 3x + 3x = c

    Solve the first for a variable: x = a + z - (b/2)
    Substitute into the other:

    2a + 3b - 2c = 0

    There is a relationship. I tried a = b = 1 and c = 5/2.

    Why worry about it when you can PROVE it!
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