Linear algebra is the sector of mathematics regarding systems of first-degree equations, such as the following:
This system of equations has a solution to certain values (that is, 
). In addition to being useful for solving systems of equations, the concepts and methods of linear algebra are also useful for representing and manipulating geometrical entities.
In particular, any position on a plane can be represented by two coordinates, x and y, and any position in space can be represented by three coordinates, x, y, and z. In addition, any translation of a position on a plane can be represented by two coordinates, Δx and Δy, and any translation of a position in space can be represented by three coordinates, Δx, Δy, and Δz.
For example, consider two positions on a plane:
- p1: Its coordinates are x = 4, y = 7.
- p2: Its coordinates are x = 10, y = 16.
Consider two translations on that plane:
- t1: Its coordinates are
. - t2: Its coordinates...
