The matrix algebra is used to solve systems of linear equations. In fact it is used in various mathematical procedures as the solution of a set of nonlinear equations, interpolation, integration and differentiation which are reduced to a set of linear equations.
SIMPLE GAUSS
The method of Gauss to be the German mathematician Johann Carl Friedrich Gauss, is a generalization of the reduction method, which we use to eliminate an unknown quantity in the systems of two equations with two unknowns. It consists of the successive application of the method of reduction, using the criteria of equivalence of systems, to transform the augmented matrix with independent terms in a triangular matrix, so that each row (equation) have a mystery unless the immediately preceding . This provides a system, which we call step, such that the last equation has a single unknown, the last but two unknowns, the penultimate three unknowns, ..., and the first all unknowns.
The operations we can do this matrix to transform the initial system into an equivalent are:
• Multiply or divide a row by a nonzero real number.
• Add or subtract a row another row.
• Add a row another row multiplied by a nonzero number.
• Change the order of the rows.
• Change the order of the columns that correspond to the unknowns of the system taking into account the changes made at the time of writing the new equivalent.
• Delete rows that are proportional or linear combination of others.
• Delete rows zero (0 0 0 ... 0).
See the example in the following document..
Example method of gauss
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GAUSS-JORDAN
This method is a variant of Gauss elimination method. The main difference with this is that when a mystery is removed from an equation in the Gauss-Jordan, this is eliminated in all equations of the system rather than being limited to the subsequent equations.
The method generates an identity matrix and therefore do not need the back substitution process. It should be noted that the method can present the same difficulties that the method of simple Gaussian elimination.
Gauss jordan
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SPECIAL METHODS
Arrays are widely used in computing, ease and lightness to manipulate information. In this context, the best way to represent graph, and are widely used in the numerical calculation.
Attached is a presentation with an explanation and rationale of two methods empeciales:
• Thomas Method
• Cholesky Method
These two methods are easy to program in any programming language, Microsoft Excel is recommended.
Cholesky method and Thomas
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REFERENCES:
(1)NUMERICAL METHODS FOR ENGINEERS WITH PERSONAL COMPUTER APPLICATIONS. STEVEN C. Chapra / Raymond P. CANALE
(2) internet-google.
(3)Enciclopedia libre wikipedia
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