Gauss - ME 210 Applied Mathematics for Mechanical Engineers...

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ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Gauss(ian) Elimination This is a systematic method in which (the coefficient of the) 1 st variable is eliminated (made equal to zero) from the (m–1) equations first, the 2 nd variable is eliminated from the last (m–2) equations then, and this process is continued until no more variable and/or equation is left. Then, the solution is obtained in the reverse order starting from the last one by a simple back substitution . This is a powerful method which also yields all the information on the consistency of equations as well as the uniqueness of the solution, if exists. The method has several variants and some advanced versions. However, a very basic version of it will be covered here.
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ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 The procedure is applied to the augmented matrix [A ¦ b] by performing a set of basic (elementary) row operations , only such that the matrix [A ¦ b] will be transformed into what is so-called as the row echelon form in which all elements of [C] = [A ¦ b] below its elements c ii {i = 1, 2, …, min(m,n+1)} become zero.
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Gauss - ME 210 Applied Mathematics for Mechanical Engineers...

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