# Linear Algebra Examples

Rewrite the vector set as a matrix.

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

This expression is the solution set for the system of equations.

Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.

Express the vector as a linear combination of column vector using the properties of vector column addition.

The null space of the set is the set of vectors created from the free variables of the system.