APPENDIX

Consider the set of equations

(A.1)

which can be expressed as

(A.2)

or

(A.3)

where

(A.4)

(A.5)

(A.6)

The solution is represented by

(A.7)

where

(A.8)

denotes the inverse matrix of A to be determined. We shall use Cramer’s rule to find the inverse matrix. Applying Cramer’s rule (Kreyszig, 1979) to (A.2), we have x_{1}:

(A.9)

If we wish to find b_{ij} in terms of a_{ij}, b_{ij} may be expressed as

Similarly,

(A.13)

(A.17) ...