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Math Help - Another set of matricies, but a different way of doing it.

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    Another set of matricies, but a different way of doing it.

    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!!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by snakeman11689 View Post
    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!!
    augment your system in a matrix

    \begin{array}{ccc|c} 2 & 1 & -1 & a \\ 1 & 2 & 1 & b \\ 5 & 4 & -1 & c \\ \hline \end{array}

    now find the reduced row echelon of the 3x3 matrix, you will be able to see what conditions on a, b and c make the system consistent (chances are you get a row of zeros with 2a + b - c in the last entry, so that must be zero as well, try it!)
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