Systems

Terms

Triangular System: n equations and n variables, like this example where n=3

$$\begin{array}{rl}2x_1-2x_2+3x_3& =3\\ 3x_2+2x_3& =21\\ 5x_3& =15\end{array}$$

Echelon System: A system of m linear equations in n variables is called an echelon system if. m ≤ n. Every variable is the leading variable of at most one equation. Every leading variable is to the left of the leading variables of all lower equations.

$$\begin{array}{rl}6x_1+x_2-3x_4& =11\\ 3x_2-4x_3+5x_4& =6\\ 2x_3-4x_4& =-3\end{array}$$

Back Substitution: The intuitive method of solving a triangular system, going from the bottom to the top so that the equation with one variable is solved first.