# Linear Algebra Examples

Step 1

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

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

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

Replace (row ) with the actual values of the elements for the row operation .

Simplify (row ).

Step 5

Pivot columns are the columns, which contains pivot positions, so those pivot columns are .

Step 6

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