# 1.1 Systems of Linear Equations

## 11 terms

### 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

### system of linear equations

a collection of one or more linear equations involving the same set of variables

### 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. the solution set is empty when the linear system is inconsistent

### equivalent

linear systems with the same solution set

### consistent

a linear system with at least one solution

### inconsistent

a linear system with no solutions

### coefficient matrix

a matrix whose entries are the coefficients of a system of linear equations

### augmented matrix

a matrix made up of a coefficient matrix for a linear system and one or more columns to the right. each extra column contains the constants from the high side of a system with the given coefficient matrix

### size

two numnbers written in the form m x n that specify the number of rows (m) and columns (n) in the matrix

### mxn matrix

a matrix with m rows and n columns