In essence, linear algebra allows us to extend the concept of dimension beyond the usual 1-, 2- and 3-dimensional spaces. More specifically, we define the dimension of an equation to be the number of independent variables it contains, For example if f(x_{1},x_{2},x_{3},x_{4}) and x_{1},x_{2},x_{3} and x_{4} are independent variables then the domain of f is 4-dimensional even though geometrically speaking there is no 4th dimension. So rather than talk about y = f(x) we, instead, "invent" a new variable (x_{1},x_{2},x_{3},x_{4}) which we denote by a symbol such as __ X__. We refer to (x

_{1},x

_{2},x

_{3},x

_{4}) as a 4-tuple; and more generally, we refer to (x

_{1},x

_{2},x

_{3},x

_{4}, ...x

_{n}) as an n-tuple. In this context linear algebra is a study of the arithmetic of n-tuples.