Chapter 3: Determinants Flashcards
The __________ is a scalar (number), obtained from the elements of a matrix by specified, operations,
which is characteristic of the matrix.
determinant of a matrix
The determinant of a matrix is a _______, obtained from the elements of a matrix by specified, operations,
which is characteristic of the matrix.
scalar (number)
The determinants are defined only for _______.
square matrices
The _________ of the element aij in a given determinant is the determinant of order (n-1 x n-1)
obtained by deleting the ith row and jth column of 𝐴𝑛𝑥𝑛
minor Mij
The scalar Cij=(-1)^(i+j) Mij are called the ______ of the element aij of the matrix A
cofactor
The value of the determinants can also be found by its ____________ or cofactors
minor elements
The value of the determinant can be found by __________ it from any row or column
expanding
_____________ the corresponding rows and columns of a determinant does not change its value
Interchanging
If two rows or two columns of a determinant are interchanged, the sign of the determinant is
changed but its ___________ is unchanged.
absolute value
If every element of a row or column of a determinant is ______, the value of the determinant is zero.
zero
If two rows or columns of a determinant are _________, the value of the determinant is zero
identical
If every element of a row or column of a determinant is multiplied by the ___________, the
value of the determinant is multiplied by that constant
same constant K
The value of a determinant is not changed if each element of any row or of any column is added to
(or subtracted from) a ____________ of the corresponding element of another row or column.
constant multiple
The determinant of a _____________ is equal to the product of its diagonal elements.
diagonal matrix
The determinant of the product of two matrices is equal to the ___________ of the
two matrices, that is |AB| = |A||B|.
product of the determinants
