Therefore the system has an unique solution given by
(*x*,*y*,*z*)=(2,3,3).

The solution set of the given system is empty.

We see already that the system has an infinity of solutions.

This matrix is associated to the system of equations:

The solution set of the given system is: .

Suppose that *A* is in row-echelon form. An unknown in the column of whom there is a leading coefficient is called
**a principal unknown**; otherwise, it is called **a free unknown**. In example 3.4, the
unknowns *x* and *y* are principal, and the unknown *z* is free.

The augmented matrix *A* of this system is the matrix given in Example 2.6, i.e.

The row-reduced matrix

Thus, the given system of equations is equivalent to the following system:

The unknowns