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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 Summary

Gaussian elimination is utilized on the augmented matrix.

Solution Preview

The system is

We use Gaussian elimination on the augmented matrix as follows.

Thus we have
(a) The ...

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