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    Systems of Equations : Triangular Form and Matrices

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    1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent.

    1 5 2 -6
    0 4 -7 2
    0 0 5 0

    2) Is (3,4,-2) a solution of the following system?

    5xsub1 - xsub2 +2xsub3 = 7
    -2xsub1 + 6xsub2 +9xsub3 = 0
    -7xsub1 + 5xsub2 -3xsub3 = -7

    3) For what values of h and k is the following system consistent?

    2xsub1 - xsub2 = h
    -6xsub1 +3 xsub2 = k

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    Solution Preview

    1. The corresponding linear system is
    Then we get z=0, y=0.5 and x=-8.5
    So we get a unique solution ...

    Solution Summary

    Questions involving systems of equations, matrices and consistency are concisely answered.