APSC 1073 Lecture Notes - Lecture 1: Coefficient Matrix, Lincoln Near-Earth Asteroid Research
Document Summary
A system of linear equations is a system of form: xa. That is to say it has m equations and n unknowns. Any system of linear equations can be written in the matrix form ax = b where a is the coefficient matrix, x is the column matrix of the variables, and b is the column matrix of the independent terms. To solve a system of linear equations is to find, if they exist, the real numbers that can take the unknowns so that all the equations are satisfied at the same time. The systems of linear equations can be classified, as a function of their solutions, as follows: compatible and incompatible. In addition, a system can not have 2, 3, 4, , k solutions. Consequently, compatible systems may be: determined: the solution is unique, indeterminate: they have infinite solutions. The incompatible: they do not support any solution.
