**Linear algebra originated as the study of linear equations and the relationship between a number of variables.** Linear algebra specifically studies the solution of simultaneous linear equations.

A linear equation is defined as a mathematical concept in which no variable is multiplied by itself or any other variable. For instance, the equation 4x + 2y - z = 0 is a linear equation in three variables, while the equation 2x - y = 7 is a linear equation in two variables. From linear algebra emerges two important concepts: vectors and matrices. The vector corresponds to directed line segments, and the matrix finds the coefficients of a simultaneous equation.