Matrices: Anyone have a real-life problem that uses matrices / linear systems of equations? Looking for something beyond a contrived textbook problem concerning jelly beans. Not just matrix manipulation for it's own sake.
I know matrix math is used in real life applications (finance, science, manufacturing, optimizing, etc) ... to solve linear systems of equations. Has anyone ever used this Math to solve a real problem at work, etc? come across a real example? Thanks!
 A: Here's an example from structural engineering:
You have a multiple degree-of-freedom system, and each system can be modeled as a spring-mass-damper system with a forcing term. These degrees of freedom are coupled.
If you write out the equations, you realize that the same terms appear in every equation. Then, voila! You have a matrix differential equation.
Then again, maybe this is contrived, since my work involves modeling these types of systems!
A: Let's say that you want to start a public works company, but don't know how high/low to make your bids to the city for projects. (Note: a "bid" lists the type and number of goods/services and the total cost, not the price per good)
If you can find sufficiently many past bids (with sufficiently many of the goods/services that you would offer) from a single competitor, you can solve a matrix equation to determine what this competitor charges for their goods/services. 
(Here I make some assumptions about linearity)
A: Look up a linear programming/optimization book.  I seem to recall an example where Delta airlines used LP (based on matrix arguments) to significantly reduce costs.
A: I use matrices in various programming situations. In the short and simple, arrays, structures, and objects are all matrix-like implementations. They sure make handling multi-variable systems easier.
Will Jagy might leave his cave from time to time.
