An equation like ax = b is called a equation. It is a degree equation in one . The solution of this equation may be interpreted in a cartesian coordinate system as the point of two lines. The solution of this equation is a in the real line, while the solutions of a linear equation in two unknowns can be represented as a in the plane and those of a linear equation in three unknowns as a in tridimensional space. A linear equation in two unknowns has always many solutions. A system of two linear equations in two unknowns may have solutions, only solution or many solutions. The system has no solutions if the two equations represent lines.
A matrix is a rectangular of real numbers. Matrix multiplication is associative, but not always .
Given a linear system of m equations in n unknowns, the matrix whose entries are all the coefficients and constants of the system is called the matrix of the system. If a matrix is in row-echelon form the leftmost non zero entry of a row is called a , and the number of these leading elements of the rows is called the of the system. The algorithm used to reduce matrices in row-echelon form is called the - algorithm. A system that has no solutions is called .