Linear Algebra Concepts

Front

linear equation

Back

An equation involving linear expressions.

Front

coefficient

Back

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Front

system of linear equations, linear system

Back

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

Front

solution, solution set

Back

The set of all possible values that satisfy a given set of equations.

Front

equivalent (linear systems)

Back

Two systems of linear equations that have the same solution set.

Front

consistent, inconsistent

Back

A system of equations is consistent if it has at least one solution; it is inconsistent if it has no solution.

Front

coefficient matrix

Back

A matrix consisting of the coefficients of the variables in a set of linear equations.

Front

augmented matrix

Back

A matrix obtained by appending the columns of two matrices, typically used to represent a system of linear equations.

Front

elementary row operations

Back

Operations including row switching, row multiplication, and row addition used to manipulate matrices.

Front

row equivalent (matrices)

Back

Two matrices are row equivalent if one can be transformed into the other by a sequence of elementary row operations.