Matrix and determinants are actually very useful in engineering. I am going to give you a good personal example. I am a chemical engineering student, and when I took my final this past semester for my chemical processes class one of the problems had certain substances going into a reactor and came out of the reactor as different chemicals (they reacted). As part of the procedure used to determine the mass of the outcoming materials you do a mass balance (actually I did an atomic balance because atoms can not be created nor destroyed), in my mass balance I had three equations and two unknowns. At the time I was taking an engineering math course where I learned about matrices and determinants, therefore with what I learned I placed my equations as a "system of matrices" one on top of the others and reduced to "row echelon form" and was able to find all masses individual for each of the compounds. I hope this helped, and if you have any questions dont hesitate to consult with me....Chem Boy.
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