Explore BrainMass

Explore BrainMass

    Gaussian elimination on the augmented matrix

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com December 15, 2022, 8:13 pm ad1c9bdddf

    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.