CH 3 - DETERMINANTS Flashcards
is a scalar (number), obtained from the elements of a matrix by specified, operations, which is characteristic of the matrix.
DETERMINANT OF A MATRIX
____________ 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 𝐴𝑛𝑥
The minor Mij
are called the cofactor of the element aij of the matrix A
scalars Cij = (-1)^i+j Mij
the value of the determinant can be found by _____ it from any row or column
expanding
interchanging the corresponding rows and columns of of a determinant ____________.
does not change its value
If two rows or two columns of a determinant are interchanged, _____________.
the sign of the determinant is changed but its absolute value is unchanged.
If every element of a row or column of a determinant is zero, _____________________.
the value of the determinant is zero.
If two rows or columns of a determinant are identical, __________________.
the value of the determinant is zero.
If every element of a row or column of a determinant is multiplied by the same constant K, _____________.
the value of the determinant is multiplied by that constant
The value of a determinant is __________ if each element of any row or of any column is added to (or subtracted from) a constant multiple of the corresponding element of another row or column.
not changed
The determinant of a diagonal matrix is equal to the __________________.
product of its diagonal elements
The determinant of the product of two matrices is equal to the __________________, that is |AB| = |A||B|.
product of the determinants of the two matrices
The determinant in which each element in any row, or column, consists of two terms, then the determinant can be __________________.
expressed as the sum of two other determinants
