23 terms

Address

The location of an entry in a matrix, given by the row and column in which the entry appears. In matrix A, the address of the entry in row i and column j is a(ij).

Augmented Matrix

A matrix that consists of the coefficients and the constant terms in a system of linear equations.

Coefficient Matrix

The matrix of the coefficients of the variables in a linear system of equations.

Constant Matrix

The matrix of the constants in a linear system of equations.

Cramer's Rule

A method of solving systems of linear equations by using determinants.

Determinant

A real number associated with a square matrix.

Dimensions (of a matrix)

A matrix with m rows and n columns has dimensions m x n.

Entry

Each value in a matrix; also called an element.

Main Diagonal (of a matrix)

The diagonal form the upper left corner to the lower right corner of a matrix.

Matrix

A rectangular array of numbers.

Matrix Equation

An equation of the form AX=B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix of a system of equations.

Matrix Product

The product of two matrices, where each entry in P(ij) is the sum of the products of consecutive entries in row i in the matrix A and column j in the matrix B.

Multiplicative Identity Matrix

A square matrix with 1 in every entry of the main diagonal and 0 in every other entry.

Multiplicative Inverse (of a square) Matrix

The multiplicative inverse of square matrix A, if it exists, is notated A(-1), where the product of A and A(-1) is the identity matrix.

Reduced Row-Echelon Form

A form of an augmented matrix in which the coefficient columns form an identity matrix.

Reflection Matrix

A matrix used to reflect a figure across a specified line of symmetry.

Rotation Matrix

A matrix used to rotate a figure about the origin.

Row Operation

An operation performed on a row of an augmented matrix that creates an equivalent matrix.

Row Reduction (method)

The process of performing elementary row operations on an augmented matrix to transform the matrix to reduced row echelon form.

Scalar

A number that is multiplied by a matrix.

Square Matrix

A matrix with the same number of rows as columns.

Translation Matrix

A matrix used to translate points on the coordinate plane.

Variable Matrix

The matrix of the variables in a linear system of equations.