Vocabulary: Linear Equations in Linear Algebra

Systems of Linear Equations

Linear Equation

An equation that represents a straight line in a space and involves variables with no powers higher than one.

Coefficients

The numerical values that multiply the variables in a linear equation.

System of Linear Equations

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

Linear System

Another term for a system of linear equations, often used interchangeably.

Solution

A set of values for the variables that satisfies all equations in a system of linear equations.

Solution Set

The complete collection of all possible solutions to a system of linear equations.

Equivalent

Two systems of equations or matrices are equivalent if they have the same solution set.

Consistent

A system of equations is consistent if it has at least one solution.

Inconsistent

A system of equations is inconsistent if it has no solution.

Matrix

A rectangular array of numbers used to organize data or represent systems of equations.

Coefficient Matrix

A matrix formed by the coefficients of the variables in a system of linear equations.

Matrix of Coefficients

Another name for the coefficient matrix, emphasizing its role in representing equation coefficients.

Augmented Matrix

A matrix that includes both the coefficients and the constant terms from a system of linear equations, separated by a vertical line or column.

m×n Matrix

A matrix with m rows and n columns.

Size of Matrix

The dimensions of a matrix, given as the number of rows m by the number of columns n.

Row Equivalent

Two matrices are row equivalent if one can be transformed into the other using row operations.