VIAS Encyclopedia provides a collection of tables and definitions commonly needed in science and engineering. |
![]() |
Home ![]() ![]() ![]() |
||||||||||
See also: Matrix Determinant | ||||||||||
![]() ![]() ![]() ![]() ![]() ![]() |
||||||||||
Matrix Determinants
|
![]() |
a11
a21 |
a12
a22 |
![]() |
be an arbitrary matrix of order 2. Then its determinant is calculated
as the product of the principal diagonal minus the product of the other
diagonal, formally a11a22
-
a12
a21.
Determinant of matrices of order 3 (Sarrus' Rule)
Let
![]() |
a11
a21 a31 |
a12
a22 a32 |
a13
a23 a33 |
![]() |
be an arbitrary matrix of order 3. Then its determinant is calculated
as the sum of the product of all "extended" falling (including the principal)
diagonals minus the sum of the product of all "extended" rising diagonals,
formally (a11a22
a33
+ a21
a32
a13
+ a31
a12
a23)
- (a31
a22
a13
+ a21
a12
a33
+ a11
a32
a23). This rule is easier to understand when we color
the relevant diagonals:
Example: determinant of a matrix of order 3
Let
Then