Linear Algebra Vocabulary

Front 1

linear equation

Back 1

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

Front 2

system of linear equations

Back 2

A collection of one more more linear equations involving the same set of variables, say x1,.....,xn

Front 3

solution of a linear system

Back 3

A list of numbers (s1,...,sn) that makes each equation in the system a true statement when the values of the set are substituted in respectfully.

Front 4

solution set

Back 4

The set of all possible solutions of a linear system. The solution set is empty when the linear system is inconsistent.

Front 5

equivalent linear systems

Back 5

Linear systems with the same solution set

Front 6

consistent linear system

Back 6

A linear system with with at least one solution

Front 7

inconsistent linear system

Back 7

A linear system with no solution

Front 8

matrix

Back 8

A rectangular array of numbers

Front 9

coefficient matrix

Back 9

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

Front 10

augmented matrix

Back 10

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

Front 11

size of a matrix

Back 11

Two numbers, written in the form "m x n", that specifiy the number of rows (m) and columns (n) in the matrix

Front 12

row equivalent matrices

Back 12

Two matrices for which there exists a finite sequence of row operations that transforms one matrix into the other.