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# AR Linear Algebra

### Linear Algebra

linear equation An equation that can be qritten in the form a1x1 + a2x2 + ... + anxn = b, where b and the coeffiecients a1,...,an are real or complex numbers
augmented matrix a matrix made up of a coefficient matrix for a linear system and one or more columns to the right.
linear system A collection of one or more linear equations involving the same variables, say x1,...,xn
solution a list of numbers that makes each equation in the system a true statement when the values s1...sn are substituted for x1,...xn
solution set the set of all possible solutions of a linear system. The solution set is empty when the linear system is inconsistent
equivalent systems linear systems with the same solution set
basic variable a variable in a linear system that corresponds to a pivot column in the coefficient matrix
free variable any variable in a linear system that is not a basic variable
full rank matrix an m x n matrix whose rank is the smaller of m and n
kernel the set of x in V such that T(x)=0
Created by: aelkins