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    Gaussian elimination on the augmented matrix

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    Consider the following system

    x_1 + x_2 + 2x_3 = a
    x_1 + x_3 = b
    2x_1 + x_2 + 3x_3 = c

    a) Find the echelon form of the system

    b) Find conditions (if possible) on the numbers a, b, and c so that the system has no solution, a unique solution, or infinitely many solutions.

    c) Find specific values for a, b, and c for which the system has infitely many solutions. Using these values, identify the leading variable(s) and nonleading variable(s) of the corresponding system. Then describe the solutions parametrically.

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    Solution Preview

    The system is

    We use Gaussian elimination on the augmented matrix as follows.

    Thus we have
    (a) The ...

    Solution Summary

    Gaussian elimination is utilized on the augmented matrix.

    $2.49

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