# Precalculus Examples

,

Write the system of equations in matrix form.

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 ).

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 ).

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 ).

Use the result matrix to declare the final solutions to the system of equations.

Rewrite the equation as .

Since , there are no solutions.

No solution

No solution

There is not a transformation of the vector that exists because there was no unique solution to the system of equations. Since there is no linear transformation, the vector is not in the column space.

Not in the Column Space