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Gaussian Elimination

Gaussian EliminationCarl Friedrich Gauss (1777-1855)German mathematician and scientist,contributed to number theory, statistics, algebra, analysis, differential geometry, geophysics, electrostatics,astronomy, optics24/45 Gaussian Elimination Method: This is aGEM of amethodto solve a system of linear that a system ofmlinear equations innunknownsx1,..,xnis of the forma11x1+a12x2+..+a1nxn=b1a21x1+a22x2+. .+a2nxn= ..am1x1+am2x2+..+amnxn=bmwhereaij(1 i m, 1 j n) andbi(1 i m)are known observation: Operations of three types onthese equations do not alter the solutions :1. Interchanging two Multiplying all the terms of an equation by a Adding to one equation a multiple of Elimination Method: This is aGEM of amethodto solve a system of linear that a system ofmlinear equations innunknownsx1.

differential geometry, geophysics, electrostatics, astronomy, optics 24/45. ... these equations do not alter the solutions: 1.Interchanging two equations. 2.Multiplying all the terms of an equation by a nonzero scalar. ... These are called elementary row operations.

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