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The paper describes a method of solving the system of linear algebraic equations with a real rectangular matrix. The method is based on the use of the Gram-Schmidt orthogonalization. The solution is found in the form $x=x_p+y$, $x_p$ being a particular solution of the system while $y$ belongs to the space of solutions of the corresponding homogeneous system.
[1] K. Hoffman R. Kunze: Linear Algebra. (2nd ed.), Prentice Hall of India (1972). MR 0276251
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