23 terms

address

The location of any 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 aij

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

A matrix with m rows and n columns has dimensions mxn, read m by n

entry

Each value in a matrix also called an element

main diagonal

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

matrix

A rectangular array of numbers

matrix equation

An equation of the from 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 Pij is the sum of the products of consecutive entries in row i in matrix a and column j in 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 matrix

The multiplicative invers of square matrix A, if it exists, is notated A-1s, where the product of A is A-1is the identity matrix

reduce 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 operations performed on a row of an augmented matrix that creates an equivalent matrix.

row reduction

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