Prerequisite : Gaussian Elimination to Solve Linear Equations
Introduction : The Gauss-Jordan method, also known as Gauss-Jordan elimination method is used to solve a system of linear equations and is a modified version of Gauss Elimination Method.
It is similar and simpler than Gauss Elimination Method as we have to perform 2 different process in Gauss Elimination Method i.e.
1) Formation of upper triangular matrix, and
2) Back substitution
But in case of Gauss-Jordan Elimination Method, we only have to form a reduced row echelon form (diagonal matrix). Below given is the flow-chart of Gauss-Jordan Elimination Method.
Flow Chart of Gauss-Jordan Elimination Method :
Input : 2y + z = 4 x + y + 2z = 6 2x + y + z = 7 Output : Final Augumented Matrix is : 1 0 0 2.2 0 2 0 2.8 0 0 -2.5 -3 Result is : 2.2 1.4 1.2
Explanation : Below given is the explanation of the above example.
Final Augumented Matrix is : 1 0 0 2.2 0 2 0 2.8 0 0 -2.5 -3 Result is : 2.2 1.4 1.2
- Solving System of Linear Equations : Gauss-Jordan Elimination Method can be used for finding the solution of a systems of linear equations which is applied throughout the mathematics.
- Finding Determinant : The Gaussian Elimination can be applied to a square matrix in order to find determinant of the matrix.
- Finding Inverse of Matrix : The Gauss-Jordan Elimination method can be used in determining the inverse of a square matrix.
- Finding Ranks and Bases : Using reduced row echelon form, the ranks as well as bases of square matrices can be computed by Gaussian elimination method.
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