# 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.

Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.

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

Linearly Dependent