Mathematics for Enzyme Reaction Kinetics and Reactor Performance. F. Xavier Malcata
Чтение книги онлайн.
Читать онлайн книгу Mathematics for Enzyme Reaction Kinetics and Reactor Performance - F. Xavier Malcata страница 82
![Mathematics for Enzyme Reaction Kinetics and Reactor Performance - F. Xavier Malcata Mathematics for Enzyme Reaction Kinetics and Reactor Performance - F. Xavier Malcata](/cover_pre848428.jpg)
premultiplication of both sides by
(4.173)
which is equivalent to
at the expense of Eqs. (4.24), (4.57), and (4.64). By the same token, one gets
(4.175)
from Eq. (4.170) – where premultiplication of both sides by
at the expense of Eqs. (4.24), (4.57) and (4.124); in view of the definition of identity matrix, one may rewrite Eq. (4.176) as
Insertion of Eq. (4.177) transforms Eq. (4.168) to
(4.178)
where B1,1 may be factored out as
(4.179)
in agreement with Eq. (4.76); isolation of B1,1 then becomes possible via premultiplication of both sides by ( A1,1 − A1,2
once again with the aid of Eqs. (4.61) and (4.124). One may likewise combine Eqs. (4.171) and (4.174) to get
(4.181)
with the aid of Eq. (4.24), where factoring out of B2,2 yields
again at the expense of Eq. (4.76), besides Eq. (4.8); after premultiplying both sides by ( A2,2 − A2,1
from Eq. (4.182). In view of Eq. (4.183), one may transform Eq. (4.174) as
(4.184)
whereas
results from combination of Eqs. (4.177) and (4.180); therefore, Eqs. (4.180) and (4.183)–(4.185) support reformulation of Eq. (4.87) finally to
(4.186)
since B = A−1 as per Eqs. (4.124) and (4.166). A similar conclusion on the form of A−1 can, as expected from the double equality in Eq. (4.124), be drawn if AB is replaced by BA in