APPENDIX

Consider the set of equations

(A.1) bappe001

which can be expressed as

(A.2) bappe002

or

(A.3) bappe003

where

(A.4) bappe004

(A.5) bappe005

(A.6) bappe006

The solution is represented by

(A.7) bappe007

where

(A.8) bappe008

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 x1:

(A.9) bappe009

If we wish to find bij in terms of aij, bij may be expressed as

(A.10) bappe010

(A.11)

(A.12)

Similarly,

(A.13)

(A.14)

(A.15)

(A.16)

(A.17) ...

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