# Algebra Examples

Find Pivot Positions and Pivot Columns
Step 1
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 2
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
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 4
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 5
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 6
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 7
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 8
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 9
Pivot columns are the columns, which contains pivot positions, so those pivot columns are .
Step 10
A pivot position in a matrix is a position that after row reduction contains a leading . Thus, the leading one in the pivot columns are the pivot positions.
The leading in the pivot columns are the pivot positions