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