# 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!

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possible duplicate of Applications of systems of linear equations – Rahul May 4 '12 at 18:50
No. All matrix problems are contrived. They are there as a test and a rite of passage. In centuries past, a young man could return from a solo hunt, or prove himself in battle. Now we have matrices. – Will Jagy May 4 '12 at 21:33
I suggest reading the book Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra by Jiří Matoušek: ams.org/bookstore?fn=20&arg1=stmlseries&ikey=STML-53 Real life is overrated anyway. – user31373 Jun 13 '12 at 15:04
Try reading the Wikipedia article onPage – jbc Sep 27 '12 at 12:15
Try reading the Wikipedia article on PageRank, in particular the sentence "The PageRank values are the entries of the dominant eigenvector of the modified adjcency matrix" – jbc Sep 27 '12 at 12:16

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)

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Anyone have a link to a specific example online somewhere? – JackOfAll May 4 '12 at 22:47
Can you post a simple example of this with actual numbers? – JackOfAll Jan 8 '13 at 13:54
I'll have to Work something up and edit when I'm not on a touchscreen. Stay tuned :) – The Chaz 2.0 Jan 8 '13 at 16:23

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!

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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.

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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.

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Will's comment was obviously tongue-in-cheek. – user31373 Sep 27 '12 at 17:13