Studying matricies at the moment and we were shown a problem that cannot be solved using the methods taught to us. We were asked to think about it and I've done some research but are unable to get the correct answers.

It's more of a "see what you can find out" than getting it right but I'm now curious...

Q: A group of drinkers keep a record of what they drink over the course of an evening in a bar. The following matrix shows the simultaneous system after four rounds when they drink 4 different drinks w, x, y & z...

$\displaystyle \left| \begin{matrix} 1.5 & 2 & 2.5 & 0.5 \\ 2.5 & 0.5 & 2 & 2.5 \\ 2 & 2.5 & 3 & 1\\ 1 & 2 & 0 & 2.5 \end{matrix} \right| * \left| \begin{matrix} w\\x\\y\\z\end{matrix} \right| = \left| \begin{matrix} 8.99\\10.46\\11.78\\7.99 \end{matrix} \right|$

The problems arises that it appears the drinks cost:

w = - 3.86

x= 0.60

y= 4.58

z= 4.26

Which seems that they were paid to drink drink w. What is the true price of the drinks?

So , I did some research and came accross ill-conditioned systems which carry errors. These errors can be maginifed when finding solutions. I guess that the method is beyond my course but I'd still like to know how to solve it....

Any takers?

Thanks, felix