It is often to solve math problems in a number of ways. Many times, some ways are efficient than others. For example, we can express linear systems as vectors and matrices, which have properties that we can exploit. Rather than solving for x, y, z, etc., taking the RREF (Reduced Row Echelon form) of a matrix can systematically reveal whether a system of linear equations has a unique solution. Representation of a solid such as a parallelepiped (A prism whose 6 faces are parallelograms) as three different vectors v1, v2, and v3 along the different edges of the parallelepiped, can be used to quickly evaluate the volume of that parallelepiped. However, these are only two basic applications. Linear Algebra creates many shortcuts that we will be exploring in this class.