Math Chapter 8 Vocab

zero; 0

A matrix consisting entirely of zeros is called a ___ matrix and is denoted by ___.

reduced row-echelon form

A matrix in row-echelon form is in ___ ___ ___ if every column that has a leading 1 has zeros in every position above and below its leading 1.

square

A matrix is ___ if the number of rows equals the number of columns.

row; column

A matrix with only one row is called a ___ matrix and a matrix with only one column is called a ___ matrix.

cryptogram

A message written according to a secret code is called a ___.

matrix

A rectangular array of real numbers that can be used to solve a system of linear equations is called a ___.

determinant

Both det(A) and |A| represent the ___ of the matrix A.

main diagonal

For a square matrix, the entries a11, a22, a33,...anm are the ___ ___ entries.

A-1B

If A is an invertible matrix, the system of linear equations represented by AX=B has a unique solution given by X=___.

nonsingular; singular

If a matrix A has an inverse, it is called invertible or ___; if it does not have an inverse, it is called ___.

inverse

If there exists an nxn matrix A-1 such that AA-1=In=A-1A, then A-1 is called the ___ of A.

square

In a ___ matrix, the number of rows equals the number of columns.

cofactor

The ___ Cij of the entry aij of the square matrix A is given by (-1)^(i+j)Mij.

minor

The ___ Mij of the entry aij is the determinant of the matrix obtained by deleting the ith row and jth column of the square matrix A.

augmented

The matrix derived from a system of linear equations is called the ___ matrix of the system.

coefficient

The matrix derived from the coefficients of a system of linear equations is called the ___ matrix of the system.

expanding; cofactors

The method of finding the determinant of a matrix of order 2x2 or greater is called ___ by ___.

Cramer's Rule

The method of using determinants to solve a system of linear equations is called ___ ___.

identity

The nxn matrix consisting of 1's on its main diagonal and 0's elsewhere is called the ___ matrix of order n.

Gauss-Jordan elimination

The process of using row operations to write a matrix in reduced row-echelon form is called ___ ___.

collinear

Three points are ___ if the points lie on the same line.

uncoded; coded

To encode a message, choose an invertible matrix A and multiply the ___ row matrices by A (on the right) to obtain ___ row matrices.

equal

Two matrices are ___ if all of their corresponding entries are equal.

row-equivalent

Two matrices are called ___ if one of the matrices can be obtained from the other by a sequence of elementary row operations.

scalars

When performing matrix operations, real numbers are often referred to as ___.