# 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.

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