Methods of solving systems of linear equations That is, if we modify the input, the system of linear equations to be solved will have a different vector b but the same matrix of coefficients A. ![]() ![]() The matrix of coefficients A, reflecting the intrinsic characteristics of the system, is independent of the input. Modeling linear systems gives rise to linear equations of the form Ax = b, where b is the input vector and the vector x represents the response of the system. The broad class of linear systems includes structures, elastic solids, heat flows, electromagnetic fields, electrical circuits and much more. ![]() But their most natural application in engineering is in the analysis of linear systems. Linear and algebraic equations can be found in almost all branches of numerical analysis.
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