Gauss Jordan method is commonly used to find the solution of linear simultaneous equations. In science and engineering, it is used to find the output of a chemical plant, examine a network under sinusoidal steady rate, etc.
Here’s a simple algorithm for Gauss Jordan Method along with flowchart, which show how a system of linear equations is reduced to diagonal matrix form by elementary row operations. The solution is directly and conveniently obtained by this method but requires a little more calculation.
Gauss Jordan method is a modified version of the Gauss elimination method. The Gauss Jordan algorithm and flowchart is also similar in many aspects to the elimination method. Compared to the elimination method, this method reduces effort and time taken to perform back substitutions for finding the unknowns.
In Gauss Elimination, the unknown variables are eliminated from the pivotal equation only, but in Gauss Jordan method, they are eliminated from all the equations. Before going through the algorithm and flowchart, learn how matrix is diagonalized in Gauss Jordan method?
Gauss Jordan Method Algorithm:
- Read the order of the matrix ‘n’ and read the coefficients of the linear equations.
- Do for k=1 to n
Do for l=k+1 to n+1
a[k][l] = a[k][l] / a[k][k]
End for l
Set a[k][k] = 1
Do for i=1 to n
if (i not equal to k) then,
Do for j=k+1 to n+1
a[i][j] = a[i][j] – (a[k][j] * a[i][k])
End for j
End for i
End for k
- Do for m=1 to n
x[m] = a[m][n+1]
End for m
Gauss Jordan Method Flowchart:
The flowchart is continued after “END for k”.
Here is another flowchart for Gauss Jordan method.
The aforementioned algorithm and flowchart seem simple, but Gauss Jordan method is generally considered to be a bit tedious in terms of additional calculation. Additionally, this method proves to be a effective one for a smaller system of linear simultaneous equations.
If you consider a system of 10 or 20 such equations, 500 multiplications would be required to solve the system using Gauss Jordan method. But, if you adopt Gauss Elimination method the number of multiplications required is only 333. So, Gauss Jordan is the simpler method, but requires 50% more calculation compared to the elimination method.