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Applications of Linear Algebra Chemistry:Balancing reaction equations x C 2H 6 + y O 2! z CO 2 + w H 2O system of linear equations, one equation for each element. 2x = z Linear algebra allows us to place the system of equations into a matrix and using Gaussian Elimination to solve for each unknown. This can be done by hand or more conveniently using a computer. The understanding of vector mathematics is important to the application of rotating magnetic fields.

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