# Linear Algebra Examples

Rewrite the vector set as a matrix.

Set up a system of equations based on the elements of each vector.

Multiply by to get .

Multiply by to get .

Multiply by to get .

Write the system of equations in matrix form.

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 ).

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

Subtract from both sides of the equation.

Since there are non-trivial solutions to the coefficient system, the set of polynomials is linearly dependent.

Linearly Dependent