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Consider the linear system of equations AX = Y
where
X is a n x 1 matrix of variables,
Y is a n x 1 matrix of constants, and
A is an n x n matrix of coefficients.
Provided A is not a singular matrix, A has an inverse, A-1, an n x n matrix.
Premultiplying by A-1 gives A-1AX = A-1Y or X = A-1Y, the solution to the linear system.
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