Page 549 - Modelling in Transport Phenomena A Conceptual Approach

A.9. MATRICES 529

in which the coefficients aij and the constants c+ are independent of x1,x2, ..... xn
but are otherwise arbitrary. In matrix notation, Eq. (A.9-30) is expressed as

C1
= [ c2 (A.9-31)
...
c,
or,
AX=C (A.9-32)

Multiplication of EQ. (A.9-32) by the inverse of the coefficient matrix A gives
X=A-’C (A.433)

A.9.4.1 Cramer’s rule
Cramer’s rule states that, if the determinant of A is not equal to zero, the system
of linear algebraic equations has a solution given by

(A.434)

where [AI and [Ajl are the determinants of the coefficient and substituted matrices,
respectively. The substituted matrix, Aj, is obtained by replacing the jth column
of A by the column of c’s, i.e.,

(A.9-35)

REFERENCES

Abramowitz, M. and I.A. Stegun, 1970, Handbook of Mathematical bctions,
Dover Publications, New York.

Buckler, S.J., 1969, The vertical wind profile of monthly mean winds over the
prairies, Canada Department of Transport, Tech. Memo. TEC 718.

Churchill, S.W., 1974, The Interpretation and Use of Rate Data: The Rate Con-
cept, Scripta Publishing Co., Washington, D.C.