### “Reducing the number of dimensions of the possible solution space” as a method for finding the exact solution of a system with a large number of unknowns

#### Abstract

Solving linear systems with a relatively large number of equations and unknowns can be achieved using an approximate method to obtain a solution with specified accuracy within numerical mathematics. Obtaining the exact solution using the computer today is only possible within the framework of symbolic mathematics. It is possible to define an algorithm that does not solve the system of equations in the usual mathematical way, but still finds its exact solution in the exact number of steps already defined. The method consists of simple computations that are not cumulative. At the same time, the number of operations is acceptable even for a relatively large number of equations and unknowns. In addition, the algorithm allows the process to start from an arbitrary initial *n*-tuple and always leads to the exact solution if it exists.

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DOI: http://dx.doi.org/10.24294/ijmss.v0i0.1075

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