Transcription of Gauss-Jordan Elimination Method - University of Babylon
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Gauss-Jordan Elimination Method - University of Babylon
Gauss-Jordan Elimination MethodThe followingrow operationson the augmented matrix of a system produce the augmented matrixof an equivalent system, , a system with the same solution as the original one. Interchange any two rows. Multiply each element of a row by a nonzero constant. Replace a row by the sum of itself and a constant multiple of another row of the these row operations, we will use the following notations. Ri Rjmeans: Interchange rowiand rowj. Rimeans: Replace rowiwith times rowi. Ri+ Rjmeans: Replace rowiwith the sum of rowiand times Gauss-Jordan Elimination Method to solve a system of linear equations is described in thefollowing Write the augmented matrix of the Use row operations to transform the augmented matrix in the form described below, which iscalled thereduced row echelon form(RREF).
Example 1. Solve the following system by using the Gauss-Jordan elimination method. x+y +z = 5 2x+3y +5z = 8 4x+5z = 2 Solution: The augmented matrix of the system is the following. 1 1 1 5 2 3 5 8 4 0 5 2 We will now perform row operations until we obtain a matrix in reduced row echelon form. 1 1 1 5 2 3 5 8 4 0 5 2
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