find all solutions to the system of linear equations. Use your favorite computing device to row-reduce the augmented matrices for the systems, and write the solutions as a set, using correct set notation

Contributed by Robert Beezer Statement [44] 

We form the augmented matrix of the system,

which row-reduces to

This augmented matrix represents the linear system x1 = 4, x2 =-2, 0 = 0, 0 = 0, which clearly has only one possible solution. We can write this solution set then as

For problems C30–C33, row-reduce the matrix without the aid of a calculator, indicating the row operations you are using at each step using the notation of Definition RO.