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**Hellreaver** I'm looking to understand practical applications of matrices, involving flow of water. One such question is this:

The attached figure shows known flow rates of hydro carbons into and out of a network of pipes at an oil refinery.

a) Set up a linear system whose solution provides the unknown flow rates.

b) Solve the system for the unknown flow rates.

c) Find the flow rates and directions of flow if x4=50 and X6=0.

I have attached a crudely drawn representation of the figure I am supposed to use. I know how to figure out missing values for a two dimensional figure, but I'm unsure of how to do a three dimensional one...