Analytical Geometry is the use of algebraic equations to describe and manipulate geometric shapes. This is done by assigning every point in space a set of numbers called coordinates. Geometric forms are then described by sets of coordinates that can be defined by equations relating coordinate points. Analytical geometry is a very powerful tool allowing us to describe and manipulate physical shapes with mathematics.
Linear algebra plays a central role in almost all parts of modern tech-
nology. Systems of linear equations involving hundreds, thousands, even billions
of unknowns are solved every second of every day in all corners of the globe (Smith 7).
Linear Algebra is the mathematics of Straight lines, flat planes, and their higher dimension cousins. It turns out that there is no limit to the number of dimensions that can be handled in a system, and the same rules and properties apply. Curvy things are not handled here.