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Problem statement

Let tex2html_wrap_inline5566 , tex2html_wrap_inline5568 , tex2html_wrap_inline5570 and tex2html_wrap_inline5572 be defined as follows.





The math problem we address is:


Let A, tex2html_wrap_inline5484 , tex2html_wrap_inline5488 , tex2html_wrap_inline5492 , tex2html_wrap_inline5496 be matrices of compatible size be given. Solve tex2html_wrap_inline5584 , tex2html_wrap_inline5584 , tex2html_wrap_inline5588 , tex2html_wrap_inline5590 , and tex2html_wrap_inline5592 for a, b, c and for tex2html_wrap_inline5600 , tex2html_wrap_inline5602 , tex2html_wrap_inline5604 and tex2html_wrap_inline5606 . When can they be solved? If these equations can be solved, find formulas for the solution.

We shall make the strong assumption that each tex2html_wrap_inline5608 is invertible. While this assumption turns out to be valid, making it at this point is cheating. Ironically, we recommend strongly that the user make heavy invertibility assumptions at the outset of a session. Later, after the main ideas have been discovered, the user can selectively relax them and thereby obtain more general results.

Wed Jul 3 10:27:42 PDT 1996