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There are several ways to invert a matrix; here, we describe Gaussian elimination for the purpose of decreasing computational costs. Gaussian elimination is the combination of triangularization and back substitution. The triangularization will make all matrix elements in the lower-left part of the diagonal line zero. Consequently, the last row in the matrix will contain only one element, which is the solution for the last coefficient. This solution is substituted back into the front rows to calculate the other coefficients.
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