Solve the system of equations by the inverse matrix method

The inverse matrix method is an efficient and frequently used method for solving systems of linear equations when applying systems of linear equations to solve planning problems for various processes. It is applied in cases where the condition is met: the number of unknowns matches the number of linear equations in the system.

An important condition is compliance with the requirement regarding the determinant of the main matrix, it should not be zero. In this case, matrix A corresponds to the inverse matrix A–1. In matrix form, systems of linear equations are written as a matrix equation: A×X = In.

The next step performed by the online calculator script is the operation of multiplying both the left and right parts of the equation by matrix A–1 on the left. As a result of transformations, the final calculation equation for computing the data column with unknowns X is obtained = A–1×In.