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Unformatted text preview: The Gauss-Jordan Method a quick introduction We are interested in solving a system of linear algebraic equations in a sys- tematic manner, preferably in a way that can be easily coded for a machine. The best general choice is the Gauss-Jordan procedure which, with certain modifications that must be used to take into account problems arising from specific difficulties in numerical analysis, can be described very easily. To- gether with a couple of examples and a couple of exercises that you can do by following the given examples, it is easily mastered. The idea is to start with a system of equations and, by carrying out certain operations on the system, reduce it to an equivalent system whose solution is easily found. It is based on three observations: 1. For a given system, it does not matter in which order the equations are listed; 2. The system remains unchanged if one equation is multiplied on both sides by a non-zero scalar; 3. If we alter replace one equation by the sum of that equation and a scalar multiple of another, then the system is unchanged.scalar multiple of another, then the system is unchanged....
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