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Gauss-Jordan Method for Linear Systems | Numerical Methods Lab
Numerical Methods - Gauss-Jordan Method

Lab 3: Gauss-Jordan Method for Systems of Linear Equations

Lab 3: Solution of Systems of Linear Equations using Gauss-Jordan Method

Experiment Information

Experiment: Solution of Systems of Linear equations using Gauss-Jordan method

Course Code: Numerical Methods

Description: Complete lab report covering theory, algorithm, Python implementation and analysis of Gauss-Jordan elimination method

Prepared by: Important Notes Team

Complete Lab Report PDF

1. Theory of Gauss-Jordan Elimination Method

1.1 Mathematical formulation of the method

1.2 Comparison with Gaussian elimination

1.3 Advantages of reduced row echelon form

2. Algorithm

2.1 Step-by-step elimination procedure

2.2 Pivoting strategies

2.3 Computational complexity analysis

3. Implementation

3.1 Python code with numpy

3.2 Input/output specifications

3.3 Handling special cases

4. Observations

4.1 Data recording table

4.2 Sample calculations

4.3 Verification of results

5. Results

5.1 Solution accuracy

5.2 Error analysis

5.3 Comparison with other methods

6. Discussion

6.1 Advantages and limitations

6.2 Numerical stability considerations

6.3 Applications in engineering problems

Digitized lab report prepared by Important Notes Team

Python Implementation of Gauss-Jordan Method

gauss_jordan.py
import numpy as np

n = int(input("No. of Unknowns:"))
A = np.zeros((n, n+1), dtype=float)

print("Enter the elements row-wise:")
for i in range(n):
    rowData = input(f"Row{i+1}:").split()
    if len(rowData) != (n+1):
        raise Exception("Error in row and column")
    A[i] = np.array(rowData, dtype=float)

m = A.shape[0]
n = A.shape[1]

if n != m + 1:
    raise Exception("error")

for j in range(m):
    if abs(A[j, j]) < 5e-8:
        raise Exception("Solution is unavailable")
    for i in range(m):
        if i != j:
            A[i] = A[i] - A[i, j]/A[j, j] * A[j]

x = np.zeros(m, dtype=float)
for i in range(m):
    x[i] = A[i, m]/A[i, i]
    print(f"x[{i + 1}] = {x[i]}")
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