We summarize the algorithm for performing row reduction.

At this point, we see that the reduced row echelon form of the ACM allows us to solve the system. However, we have not discussed how the transition to that form is accomplished. The following algorithm describes that process.
Step 1
Determine the left-most column containing a non-zero entry (it exists if the matrix is non-zero).
Step 2
If needed, perform a type I operation so that the first non-zero column has a non-zero entry in the first row.
Step 3
If needed, perform a type II operation to make that first non-zero entry 1 (the leading 1 in the first row).
Step 4
Perform type III operations to make the entries below this leading 1 equal to 0.
Step 5
Repeat the previous four steps on the submatrix consisting of all except the first row, until reaching the end of the rows.
Step 6
For each row containing a leading 1, proceed upward using type III operations to make zero any entry appearing above a leading 1.

To summarize,

Use the row reduction algorithm detailed above to put the following ACMs in reduced row echelon form. Use your answer to find the complete set of solutions to the system of equations the ACM represents.