Reduce the matrix to reduced row-echelon form

Question

-3 1 -3 21
 2  3  3 -6
 2  0 -3 3

Answer 1

The TI-84 calculator does rref very well.

Just input the matrix  using 2ndMatrix / edit

Then grab the rref function from the catalog.  Its argument is the name of the matrix you used above.

The result is

 

1 0 0 -3

0 1 0  3

0 0 1 -3

 

The fact that the last row starts with 0 0 1  means that the system was not singular.