# Algebra Examples

Step 1
Assign the matrix the name to simplify the descriptions throughout the problem.
Step 2
Find the reduced row echelon form of the matrix.
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 ).
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 ).
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 ).
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 ).
Step 3
represents the set of the pivot columns in the row-reduced form of the matrix.
Step 4
Rank is the dimension of the column space of .
Step 5
The rank of is .