Assign the matrix the name to simplify the descriptions throughout the problem.
Find the reduced row echelon form of the matrix.
Exchange row and row to organize the zeros into position.
Perform the row operation on (row ) in order to convert some elements in the row to .
Replace (row ) with the row operation in order to convert some elements in the row to the desired value .
Replace (row ) with the actual values of the elements for the row operation .
Simplify (row ).
represents the set of the pivot columns in the row-reduced form of the matrix.
Rank is the dimension of the column space of .
The rank of is .