Terms

_________ is the difference of the products of the two diagonals of the matrix

determinant

three operations correspond to ________ which produces a new augmented matrix corresponding to a new system of linear equations

elementary row operations

the method of finding the determinant of a matrix of order 2 x 2 or greater is called _____________

expanding by cofactors

Definition of Matrix

for all m and n there exists Z where m = # of rows and n= # of columns

the entry in the __th row and ___th column is denoted by the ______________ notation a___

i; j; double subscript; ij

the nxn matrix that consists of 1's on its main diagonal and 0's everywhere else is called the _________

identity matrix of order n

if a matrix A has an inverse, A is called ___________; otherwise, A is called _________

invertible (nonsingular) ; singular

for each row that does not consist entirely of zeros, the first nonzero entry is 1: _______

leading 1

for a square matrix, the entried a11, a22..... are the _________entries

main diagonal

the plural of matrix is ________

matrices

______ is a rectangular array of real numbers

matrix

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

matrix

a matrix having m rows and n columns is said to be of __________

order mxn

if every column that has a leading 1 has zeros in every position above and below its leading 1 is called __________

reduced row-echelon form

a row that has only one row is called a ________ and a matrix that has only one column is called a __________

row matrix; column matrix

two matrices are ________ if one can be obtained from the other by a sequence of elementary row operations

row-equivalent

in operations with matrices, numbers are usually referred to as _______

scalars

if m=n, the matrix is _______ of order n

square

to encode a message, choose an invertible matrix A and multiply the ______ row matrices by A to obtain _____ row matrices

uncoded; coded

who was the British mathematician who invented matrices; he and two Americans, ______ and _______, are credited with developing Matrix algebra

Arthur Cayley; Benjamin Peirce; Charles Peirce

Who were the two men who came up with the second method of elimination

Carl Friedrich Guass; Wilhelm Jordan

________ uses determinants to write the solution of system of linear equations

Cramer's Rule

__________ continues the reduction process until a reduced row-echelon form is obtained

Gauss-Jordan Elimination

the matrix derived from a system of linear equation is called the _______ matrix of the sysem

augmented

a matrix derived from a system of linear equations is the _____________ of the system

augmented matrix

the matrix derived from the coefficients of a system of linear equations is called the ________ matrix of the sytem

coefficient

the matrix derived from the coefficients of the system is the ____________ of the system

coefficient matrix

a message written according to a secret code is called a ______

cryptogram

a matrix consisting entirely of zeros is called a ______ matrix and is denoted by ______

zero; O