Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix D 277
D.3 Determinants
I Determinant of a matrix: A determinant of a matrix is, in general, a number which
is evaluated according to the rule
det (A)=|A| =
X
=1
(D.29)
The are called the co-factors which are obtained by omitting the ’th row and ’th
column (marked below in red) and multiplying by (−1) + :
11 1 1
. . .
=(−1)
¯¯¯¯¯¯¯¯¯¯¯
+ 1
. . .
1
¯¯¯¯¯¯¯¯¯¯¯
(D.30)
I
Evaluation of simple determinants:
¯
¯ = −
(D.31)
11 12 13
21 22 23 = (D.32)
¯ 31 32 33
¯¯¯¯¯¯
= 11 22 33 + 12 23 31 + 13 21 32
− ( 13 22 31 + 11 23 32 + 12 21 33 )
where we “extended” the original determinant according to the scheme
11 12 13 11 12
21 22 23 21 22
(D.33)
¯ 31 32 33
¯¯¯¯¯¯ 31 32