# Linear Algebra Examples

Assign the matrix the name to simplify the descriptions throughout the problem.

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 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 .