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.
- Gaussian Elimination to Solve Linear Equations
- Program for Muller Method
- Program for Bisection Method
- Program for Newton Raphson Method
- Program to find root of an equations using secant method
- Program for Picard's iterative method | Computational Mathematics
- Program for sum of cos(x) series
- Program to add two fractions
- Program for n-th even number
- Program to add two polynomials
- C program to calculate the value of nPr
- Program for n-th odd number
- Program to find sum of 1 + x/2! + x^2/3! +...+x^n/(n+1)!
- Program to calculate value of nCr
- Program to compare m^n and n^m
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.