Linear Algebra and its Applications

Linear equation - An equation that can be written in the form a1x1 + a2x2 + ... + anxn = b, where b and the coefficients a1, ..., an are real or complex numbers. coefficients - system of linear equations (linear system) - A collection of one or more linear equations involving the same set of variables, say, x1, ... , xn. solution - A list (s1, s2, ..., sn) of numbers that makes each equation in the system a true statement when the values s1, ..., sn are substituted for x1, ..., xn, respectively. solution set - The set of all possible solutions of a linear system. equivalent linear systems - Linear systems with the same solution set. consistent linear system - A system with at least one solution. inconsistent linear system - A system with no solutions. matrix - A rectangular array of numbers. coefficient matrix - A matrix whose entries are the coefficients of a system of linear equations.