Consider the following matrix to be an augmented matrix over the integers modulo 2, with the last column being the right hand side of the associated system five equations in seven unknowns. $x_1$, $x_2$, ..., $x_7$.

[1 0 0 0 0 0 1 1]
[1 0 1 1 0 1 1 0]
[0 0 1 0 1 0 0 0]
[1 0 0 0 1 1 0 0]
[0 1 1 1 1 1 1 1]

(a) Row reduce the system to reduced echelon form with basic variable identified from left to right, as we did in class.

(b) Describe the solution set to the system in terms of free variables. Identify the number of solutions. It is possible that your system will have no solution.