# Equations Solvers
A comprehensive Python package for matrix operations and solving linear equations. This package provides easy-to-use classes for working with 2x2 and 3x3 matrices, along with a powerful linear equation solver.
[](https://www.python.org/downloads/)
[](LICENSE.txt)
## Features
✨ **Matrix Operations**
- Addition and Subtraction
- Matrix and Scalar Multiplication
- Matrix and Scalar Division
- Determinant Calculation
- Adjoint Matrix
- Multiplicative Inverse
🔢 **Linear Equation Solver**
- Solve 2x2 and 3x3 systems
- Multiple solving methods (Cramer's Rule, Matrix Inversion)
- Parse equations from string format
- Fraction results for exact solutions
🛡️ **Robust Error Handling**
- Invalid matrix detection
- Singular matrix handling
- Division by zero protection
- Equation parsing validation
## Installation
```bash
pip install equations_solvers
```
For development installation:
```bash
git clone https://github.com/yourusername/equations_solvers.git
cd equations_solvers
pip install -e .
```
## Quick Start
```python
from equations_solvers import Matrices2x2, LinearEquationsSolver
# Create a 2x2 matrix calculator
calc = Matrices2x2()
# Define matrices
A = [[2, 3], [1, 4]]
B = [[5, 2], [3, 1]]
# Perform operations
result = calc.add(A, B)
print(result) # [[7.0, 5.0], [4.0, 5.0]]
# Solve linear equations
solver = LinearEquationsSolver("2x + 4y = 5, 3x - 3y = -1")
solution = solver.solve('cramer')
for var, val in solution:
print(f"{var} = {val}")
# Output: x = 11/18, y = 17/18
```
## Documentation
### Table of Contents
1. [2x2 Matrix Operations](#2x2-matrix-operations)
2. [3x3 Matrix Operations](#3x3-matrix-operations)
3. [Linear Equation Solver](#linear-equation-solver)
4. [Error Handling](#error-handling)
---
## 2x2 Matrix Operations
The `Matrices2x2` class provides comprehensive operations for 2x2 matrices.
### Basic Usage
```python
from equations_solvers import Matrices2x2
# Create an instance
calc = Matrices2x2()
# Define matrices
A = [[2, 3], [1, 4]]
B = [[5, 2], [3, 1]]
```
### Addition
```python
result = calc.add(A, B)
print(result)
```
**Output:**
```
[[7.0, 5.0], [4.0, 5.0]]
```
### Subtraction
```python
result = calc.subtract(A, B)
print(result)
```
**Output:**
```
[[-3.0, 1.0], [-2.0, 3.0]]
```
### Matrix Multiplication
```python
result = calc.multiply(A, B)
print(result)
```
**Output:**
```
[[19, 7], [17, 6]]
```
### Scalar Multiplication
```python
result = calc.multiply(A, num=2)
print(result)
```
**Output:**
```
[[4, 6], [2, 8]]
```
### Scalar Division
```python
result = calc.divide(A, num=2)
print(result)
```
**Output:**
```
[[1.0, 1.5], [0.5, 2.0]]
```
### Determinant
```python
det = calc.determinant(A)
print(det)
```
**Output:**
```
5.0
```
### Adjoint Matrix
```python
adj = calc.adjoint(A)
print(adj)
```
**Output:**
```
[[4.0, -3.0], [-1.0, 2.0]]
```
### Multiplicative Inverse
```python
inv = calc.multiplicative_inverse(A)
print(inv)
```
**Output:**
```
[[0.8, -0.6], [-0.2, 0.4]]
```
---
## 3x3 Matrix Operations
The `Matrices3x3` class provides comprehensive operations for 3x3 matrices.
### Basic Usage
```python
from equations_solvers import Matrices3x3
# Create an instance
calc = Matrices3x3()
# Define matrices
C = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]
D = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] # Identity matrix
```
### Addition
```python
result = calc.add(C, D)
print(result)
```
**Output:**
```
[[2.0, 2.0, 3.0], [0.0, 2.0, 4.0], [5.0, 6.0, 1.0]]
```
### Subtraction
```python
result = calc.subtract(C, D)
print(result)
```
**Output:**
```
[[0.0, 2.0, 3.0], [0.0, 0.0, 4.0], [5.0, 6.0, -1.0]]
```
### Matrix Multiplication
```python
result = calc.matrix_multiply(C, D)
print(result)
```
**Output:**
```
[[1, 2, 3], [0, 1, 4], [5, 6, 0]]
```
### Scalar Multiplication
```python
result = calc.scalar_multiply(C, 3)
print(result)
```
**Output:**
```
[[3, 6, 9], [0, 3, 12], [15, 18, 0]]
```
### Scalar Division
```python
result = calc.scalar_divide(C, 3)
print(result)
```
**Output:**
```
[[0.333, 0.667, 1.0], [0.0, 0.333, 1.333], [1.667, 2.0, 0.0]]
```
### Determinant
```python
det = calc.determinant(C)
print(det)
```
**Output:**
```
1.0
```
### Adjoint Matrix
```python
adj = calc.adjoint(C)
print(adj)
```
**Output:**
```
[[-24.0, 18.0, 5.0], [20.0, -15.0, -4.0], [-5.0, 4.0, 1.0]]
```
### Multiplicative Inverse
```python
inv = calc.multiplicative_inverse(C)
print(inv)
```
**Output:**
```
[[-24.0, 18.0, 5.0], [20.0, -15.0, -4.0], [-5.0, 4.0, 1.0]]
```
### Matrix Division
```python
result = calc.matrix_divide(C, D)
print(result)
```
**Output:**
```
[[1.0, 2.0, 3.0], [0.0, 1.0, 4.0], [5.0, 6.0, 0.0]]
```
---
## Linear Equation Solver
The `LinearEquationsSolver` class solves systems of 2x2 and 3x3 linear equations.
### Solving 2x2 Systems
```python
from equations_solvers import LinearEquationsSolver
# Define the system of equations
solver = LinearEquationsSolver("2x + 4y = 5, 3x - 3y = -1")
# Get coefficient matrix
print("Coefficient Matrix:")
for row in solver.A():
print(row)
```
**Output:**
```
Coefficient Matrix:
[2.0, 4.0]
[3.0, -3.0]
```
#### Using Cramer's Rule
```python
solution = solver.solve('cramer')
for var, val in solution:
print(f"{var} = {val}")
```
**Output:**
```
x = 11/18
y = 17/18
```
#### Using Matrix Inversion
```python
solution = solver.solve('inverse')
for var, val in solution:
print(f"{var} = {val}")
```
**Output:**
```
x = 11/18
y = 17/18
```
### Solving 3x3 Systems
```python
# Define a 3x3 system
solver = LinearEquationsSolver("3x + y - z = 10, -3x + 4y - z = 10, 3x + y + 4z = 0")
# Solve using Cramer's rule
solution = solver.solve('cramer')
for var, val in solution:
print(f"{var} = {val}")
```
**Output:**
```
x = 8/5
y = 16/5
z = -2
```
### Complete Example with Verification
```python
# System: 2x + 3y = 8, x + 4y = 10
solver = LinearEquationsSolver("2x + 3y = 8, x + 4y = 10")
# Solve
solution = solver.solve('cramer')
x_val = float(solution[0][1])
y_val = float(solution[1][1])
print(f"Solution: x = {solution[0][1]}, y = {solution[1][1]}")
# Verify
eq1 = 2 * x_val + 3 * y_val
eq2 = x_val + 4 * y_val
print(f"\nVerification:")
print(f"2x + 3y = {eq1} (should be 8)")
print(f"x + 4y = {eq2} (should be 10)")
```
**Output:**
```
Solution: x = 2/5, y = 12/5
Verification:
2x + 3y = 8.0 (should be 8)
x + 4y = 10.0 (should be 10)
```
---
## Error Handling
The package includes robust error handling for common issues.
### Singular Matrix (Non-Invertible)
```python
from equations_solvers import Matrices3x3, InvalidMatrixError
calc = Matrices3x3()
singular = [[1, 2, 3], [2, 4, 6], [3, 6, 9]]
try:
inv = calc.multiplicative_inverse(singular)
except InvalidMatrixError as e:
print(f"Error: {e}")
```
**Output:**
```
Error: Matrix is singular and cannot be inverted.
```
### Division by Zero
```python
from equations_solvers import Matrices2x2, InvalidMatrixError
calc = Matrices2x2()
A = [[2, 3], [1, 4]]
try:
result = calc.divide(A, num=0)
except InvalidMatrixError as e:
print(f"Error: {e}")
```
**Output:**
```
Error: Division by zero is not allowed.
```
### Invalid Equation Format
```python
from equations_solvers import LinearEquationsSolver
try:
# Missing equals sign
solver = LinearEquationsSolver("2x + 3y")
except Exception as e:
print(f"Error: {e}")
```
**Output:**
```
Error: Equation must contain '=': 2x+3y
```
### Inconsistent Variables
```python
try:
# Variables don't match across equations
solver = LinearEquationsSolver("x + y = 1, x + z = 2")
except Exception as e:
print(f"Error: {e}")
```
**Output:**
```
Error: Equation 2 has inconsistent variables. Expected ['x', 'y'], got ['x', 'z']
```
---
## API Reference
### Matrices2x2
**Methods:**
- `add(matrix1, matrix2)` - Add two matrices
- `subtract(matrix1, matrix2)` - Subtract matrix2 from matrix1
- `multiply(matrix1, matrix2=None, num=None)` - Multiply matrices or by scalar
- `divide(matrix, matrix2=None, num=None)` - Divide matrix by scalar or another matrix
- `determinant(matrix)` - Calculate determinant
- `adjoint(matrix)` - Calculate adjoint matrix
- `multiplicative_inverse(matrix)` - Calculate inverse matrix
### Matrices3x3
**Methods:**
- `add(matrix1, matrix2)` - Add two matrices
- `subtract(matrix1, matrix2)` - Subtract matrix2 from matrix1
- `matrix_multiply(matrix1, matrix2)` - Multiply two matrices
- `scalar_multiply(matrix, scalar)` - Multiply matrix by scalar
- `matrix_divide(matrix1, matrix2)` - Divide matrix1 by matrix2
- `scalar_divide(matrix, scalar)` - Divide matrix by scalar
- `determinant(matrix)` - Calculate determinant
- `adjoint(matrix)` - Calculate adjoint matrix
- `multiplicative_inverse(matrix)` - Calculate inverse matrix
### LinearEquationsSolver
**Constructor:**
- `LinearEquationsSolver(equations_str)` - Parse equations from string
**Methods:**
- `A()` - Get coefficient matrix
- `solve(method='cramer')` - Solve system using 'cramer' or 'inverse' method
**Returns:** List of tuples `[(variable, value), ...]`
### InvalidMatrixError
Custom exception raised for matrix-related errors.
---
## Contributing
Contributions are welcome! Please follow these steps:
1. Fork the repository
2. Create a feature branch (`git checkout -b feature/amazing-feature`)
3. Commit your changes (`git commit -m 'Add amazing feature'`)
4. Push to the branch (`git push origin feature/amazing-feature`)
5. Open a Pull Request
---
## License
This project is licensed under the MIT License - see the [LICENSE.txt](LICENSE.txt) file for details.
---
## Author
**Your Name**
- GitHub: [@Hammail-Riaz](https://github.com/Hammail-Riaz)
- Email: hammailriaz.dev@gmail.com
---
## Changelog
### Version 0.1.0 (Initial Release)
- 2x2 and 3x3 matrix operations
- Linear equation solver with multiple methods
- Comprehensive error handling
- Full documentation and examples
---
## Acknowledgments
- Built with Python 3.8+
- Inspired by linear algebra education needs
- Thanks to all contributors
---
## Support
If you encounter any issues or have questions:
- Open an issue on [GitHub Issues](https://github.com/yourusername/equations_solvers/issues)
- Check the [documentation](#documentation)
- Contact: hammailriaz.dev@gmail.com
---
**Made with ❤️ for mathematics and Python enthusiasts**
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"description": "# Equations Solvers\r\n\r\nA comprehensive Python package for matrix operations and solving linear equations. This package provides easy-to-use classes for working with 2x2 and 3x3 matrices, along with a powerful linear equation solver.\r\n\r\n[](https://www.python.org/downloads/)\r\n[](LICENSE.txt)\r\n\r\n## Features\r\n\r\n\u2728 **Matrix Operations**\r\n- Addition and Subtraction\r\n- Matrix and Scalar Multiplication\r\n- Matrix and Scalar Division\r\n- Determinant Calculation\r\n- Adjoint Matrix\r\n- Multiplicative Inverse\r\n\r\n\ud83d\udd22 **Linear Equation Solver**\r\n- Solve 2x2 and 3x3 systems\r\n- Multiple solving methods (Cramer's Rule, Matrix Inversion)\r\n- Parse equations from string format\r\n- Fraction results for exact solutions\r\n\r\n\ud83d\udee1\ufe0f **Robust Error Handling**\r\n- Invalid matrix detection\r\n- Singular matrix handling\r\n- Division by zero protection\r\n- Equation parsing validation\r\n\r\n## Installation\r\n\r\n```bash\r\npip install equations_solvers\r\n```\r\n\r\nFor development installation:\r\n```bash\r\ngit clone https://github.com/yourusername/equations_solvers.git\r\ncd equations_solvers\r\npip install -e .\r\n```\r\n\r\n## Quick Start\r\n\r\n```python\r\nfrom equations_solvers import Matrices2x2, LinearEquationsSolver\r\n\r\n# Create a 2x2 matrix calculator\r\ncalc = Matrices2x2()\r\n\r\n# Define matrices\r\nA = [[2, 3], [1, 4]]\r\nB = [[5, 2], [3, 1]]\r\n\r\n# Perform operations\r\nresult = calc.add(A, B)\r\nprint(result) # [[7.0, 5.0], [4.0, 5.0]]\r\n\r\n# Solve linear equations\r\nsolver = LinearEquationsSolver(\"2x + 4y = 5, 3x - 3y = -1\")\r\nsolution = solver.solve('cramer')\r\nfor var, val in solution:\r\n print(f\"{var} = {val}\")\r\n# Output: x = 11/18, y = 17/18\r\n```\r\n\r\n## Documentation\r\n\r\n### Table of Contents\r\n1. [2x2 Matrix Operations](#2x2-matrix-operations)\r\n2. [3x3 Matrix Operations](#3x3-matrix-operations)\r\n3. [Linear Equation Solver](#linear-equation-solver)\r\n4. [Error Handling](#error-handling)\r\n\r\n---\r\n\r\n## 2x2 Matrix Operations\r\n\r\nThe `Matrices2x2` class provides comprehensive operations for 2x2 matrices.\r\n\r\n### Basic Usage\r\n\r\n```python\r\nfrom equations_solvers import Matrices2x2\r\n\r\n# Create an instance\r\ncalc = Matrices2x2()\r\n\r\n# Define matrices\r\nA = [[2, 3], [1, 4]]\r\nB = [[5, 2], [3, 1]]\r\n```\r\n\r\n### Addition\r\n\r\n```python\r\nresult = calc.add(A, B)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[7.0, 5.0], [4.0, 5.0]]\r\n```\r\n\r\n### Subtraction\r\n\r\n```python\r\nresult = calc.subtract(A, B)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[-3.0, 1.0], [-2.0, 3.0]]\r\n```\r\n\r\n### Matrix Multiplication\r\n\r\n```python\r\nresult = calc.multiply(A, B)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[19, 7], [17, 6]]\r\n```\r\n\r\n### Scalar Multiplication\r\n\r\n```python\r\nresult = calc.multiply(A, num=2)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[4, 6], [2, 8]]\r\n```\r\n\r\n### Scalar Division\r\n\r\n```python\r\nresult = calc.divide(A, num=2)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[1.0, 1.5], [0.5, 2.0]]\r\n```\r\n\r\n### Determinant\r\n\r\n```python\r\ndet = calc.determinant(A)\r\nprint(det)\r\n```\r\n\r\n**Output:**\r\n```\r\n5.0\r\n```\r\n\r\n### Adjoint Matrix\r\n\r\n```python\r\nadj = calc.adjoint(A)\r\nprint(adj)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[4.0, -3.0], [-1.0, 2.0]]\r\n```\r\n\r\n### Multiplicative Inverse\r\n\r\n```python\r\ninv = calc.multiplicative_inverse(A)\r\nprint(inv)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[0.8, -0.6], [-0.2, 0.4]]\r\n```\r\n\r\n---\r\n\r\n## 3x3 Matrix Operations\r\n\r\nThe `Matrices3x3` class provides comprehensive operations for 3x3 matrices.\r\n\r\n### Basic Usage\r\n\r\n```python\r\nfrom equations_solvers import Matrices3x3\r\n\r\n# Create an instance\r\ncalc = Matrices3x3()\r\n\r\n# Define matrices\r\nC = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]\r\nD = [[1, 0, 0], [0, 1, 0], [0, 0, 1]] # Identity matrix\r\n```\r\n\r\n### Addition\r\n\r\n```python\r\nresult = calc.add(C, D)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[2.0, 2.0, 3.0], [0.0, 2.0, 4.0], [5.0, 6.0, 1.0]]\r\n```\r\n\r\n### Subtraction\r\n\r\n```python\r\nresult = calc.subtract(C, D)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[0.0, 2.0, 3.0], [0.0, 0.0, 4.0], [5.0, 6.0, -1.0]]\r\n```\r\n\r\n### Matrix Multiplication\r\n\r\n```python\r\nresult = calc.matrix_multiply(C, D)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[1, 2, 3], [0, 1, 4], [5, 6, 0]]\r\n```\r\n\r\n### Scalar Multiplication\r\n\r\n```python\r\nresult = calc.scalar_multiply(C, 3)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[3, 6, 9], [0, 3, 12], [15, 18, 0]]\r\n```\r\n\r\n### Scalar Division\r\n\r\n```python\r\nresult = calc.scalar_divide(C, 3)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[0.333, 0.667, 1.0], [0.0, 0.333, 1.333], [1.667, 2.0, 0.0]]\r\n```\r\n\r\n### Determinant\r\n\r\n```python\r\ndet = calc.determinant(C)\r\nprint(det)\r\n```\r\n\r\n**Output:**\r\n```\r\n1.0\r\n```\r\n\r\n### Adjoint Matrix\r\n\r\n```python\r\nadj = calc.adjoint(C)\r\nprint(adj)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[-24.0, 18.0, 5.0], [20.0, -15.0, -4.0], [-5.0, 4.0, 1.0]]\r\n```\r\n\r\n### Multiplicative Inverse\r\n\r\n```python\r\ninv = calc.multiplicative_inverse(C)\r\nprint(inv)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[-24.0, 18.0, 5.0], [20.0, -15.0, -4.0], [-5.0, 4.0, 1.0]]\r\n```\r\n\r\n### Matrix Division\r\n\r\n```python\r\nresult = calc.matrix_divide(C, D)\r\nprint(result)\r\n```\r\n\r\n**Output:**\r\n```\r\n[[1.0, 2.0, 3.0], [0.0, 1.0, 4.0], [5.0, 6.0, 0.0]]\r\n```\r\n\r\n---\r\n\r\n## Linear Equation Solver\r\n\r\nThe `LinearEquationsSolver` class solves systems of 2x2 and 3x3 linear equations.\r\n\r\n### Solving 2x2 Systems\r\n\r\n```python\r\nfrom equations_solvers import LinearEquationsSolver\r\n\r\n# Define the system of equations\r\nsolver = LinearEquationsSolver(\"2x + 4y = 5, 3x - 3y = -1\")\r\n\r\n# Get coefficient matrix\r\nprint(\"Coefficient Matrix:\")\r\nfor row in solver.A():\r\n print(row)\r\n```\r\n\r\n**Output:**\r\n```\r\nCoefficient Matrix:\r\n[2.0, 4.0]\r\n[3.0, -3.0]\r\n```\r\n\r\n#### Using Cramer's Rule\r\n\r\n```python\r\nsolution = solver.solve('cramer')\r\nfor var, val in solution:\r\n print(f\"{var} = {val}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nx = 11/18\r\ny = 17/18\r\n```\r\n\r\n#### Using Matrix Inversion\r\n\r\n```python\r\nsolution = solver.solve('inverse')\r\nfor var, val in solution:\r\n print(f\"{var} = {val}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nx = 11/18\r\ny = 17/18\r\n```\r\n\r\n### Solving 3x3 Systems\r\n\r\n```python\r\n# Define a 3x3 system\r\nsolver = LinearEquationsSolver(\"3x + y - z = 10, -3x + 4y - z = 10, 3x + y + 4z = 0\")\r\n\r\n# Solve using Cramer's rule\r\nsolution = solver.solve('cramer')\r\nfor var, val in solution:\r\n print(f\"{var} = {val}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nx = 8/5\r\ny = 16/5\r\nz = -2\r\n```\r\n\r\n### Complete Example with Verification\r\n\r\n```python\r\n# System: 2x + 3y = 8, x + 4y = 10\r\nsolver = LinearEquationsSolver(\"2x + 3y = 8, x + 4y = 10\")\r\n\r\n# Solve\r\nsolution = solver.solve('cramer')\r\nx_val = float(solution[0][1])\r\ny_val = float(solution[1][1])\r\n\r\nprint(f\"Solution: x = {solution[0][1]}, y = {solution[1][1]}\")\r\n\r\n# Verify\r\neq1 = 2 * x_val + 3 * y_val\r\neq2 = x_val + 4 * y_val\r\n\r\nprint(f\"\\nVerification:\")\r\nprint(f\"2x + 3y = {eq1} (should be 8)\")\r\nprint(f\"x + 4y = {eq2} (should be 10)\")\r\n```\r\n\r\n**Output:**\r\n```\r\nSolution: x = 2/5, y = 12/5\r\n\r\nVerification:\r\n2x + 3y = 8.0 (should be 8)\r\nx + 4y = 10.0 (should be 10)\r\n```\r\n\r\n---\r\n\r\n## Error Handling\r\n\r\nThe package includes robust error handling for common issues.\r\n\r\n### Singular Matrix (Non-Invertible)\r\n\r\n```python\r\nfrom equations_solvers import Matrices3x3, InvalidMatrixError\r\n\r\ncalc = Matrices3x3()\r\nsingular = [[1, 2, 3], [2, 4, 6], [3, 6, 9]]\r\n\r\ntry:\r\n inv = calc.multiplicative_inverse(singular)\r\nexcept InvalidMatrixError as e:\r\n print(f\"Error: {e}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nError: Matrix is singular and cannot be inverted.\r\n```\r\n\r\n### Division by Zero\r\n\r\n```python\r\nfrom equations_solvers import Matrices2x2, InvalidMatrixError\r\n\r\ncalc = Matrices2x2()\r\nA = [[2, 3], [1, 4]]\r\n\r\ntry:\r\n result = calc.divide(A, num=0)\r\nexcept InvalidMatrixError as e:\r\n print(f\"Error: {e}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nError: Division by zero is not allowed.\r\n```\r\n\r\n### Invalid Equation Format\r\n\r\n```python\r\nfrom equations_solvers import LinearEquationsSolver\r\n\r\ntry:\r\n # Missing equals sign\r\n solver = LinearEquationsSolver(\"2x + 3y\")\r\nexcept Exception as e:\r\n print(f\"Error: {e}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nError: Equation must contain '=': 2x+3y\r\n```\r\n\r\n### Inconsistent Variables\r\n\r\n```python\r\ntry:\r\n # Variables don't match across equations\r\n solver = LinearEquationsSolver(\"x + y = 1, x + z = 2\")\r\nexcept Exception as e:\r\n print(f\"Error: {e}\")\r\n```\r\n\r\n**Output:**\r\n```\r\nError: Equation 2 has inconsistent variables. Expected ['x', 'y'], got ['x', 'z']\r\n```\r\n\r\n---\r\n\r\n## API Reference\r\n\r\n### Matrices2x2\r\n\r\n**Methods:**\r\n- `add(matrix1, matrix2)` - Add two matrices\r\n- `subtract(matrix1, matrix2)` - Subtract matrix2 from matrix1\r\n- `multiply(matrix1, matrix2=None, num=None)` - Multiply matrices or by scalar\r\n- `divide(matrix, matrix2=None, num=None)` - Divide matrix by scalar or another matrix\r\n- `determinant(matrix)` - Calculate determinant\r\n- `adjoint(matrix)` - Calculate adjoint matrix\r\n- `multiplicative_inverse(matrix)` - Calculate inverse matrix\r\n\r\n### Matrices3x3\r\n\r\n**Methods:**\r\n- `add(matrix1, matrix2)` - Add two matrices\r\n- `subtract(matrix1, matrix2)` - Subtract matrix2 from matrix1\r\n- `matrix_multiply(matrix1, matrix2)` - Multiply two matrices\r\n- `scalar_multiply(matrix, scalar)` - Multiply matrix by scalar\r\n- `matrix_divide(matrix1, matrix2)` - Divide matrix1 by matrix2\r\n- `scalar_divide(matrix, scalar)` - Divide matrix by scalar\r\n- `determinant(matrix)` - Calculate determinant\r\n- `adjoint(matrix)` - Calculate adjoint matrix\r\n- `multiplicative_inverse(matrix)` - Calculate inverse matrix\r\n\r\n### LinearEquationsSolver\r\n\r\n**Constructor:**\r\n- `LinearEquationsSolver(equations_str)` - Parse equations from string\r\n\r\n**Methods:**\r\n- `A()` - Get coefficient matrix\r\n- `solve(method='cramer')` - Solve system using 'cramer' or 'inverse' method\r\n\r\n**Returns:** List of tuples `[(variable, value), ...]`\r\n\r\n### InvalidMatrixError\r\n\r\nCustom exception raised for matrix-related errors.\r\n\r\n---\r\n\r\n## Contributing\r\n\r\nContributions are welcome! Please follow these steps:\r\n\r\n1. Fork the repository\r\n2. Create a feature branch (`git checkout -b feature/amazing-feature`)\r\n3. Commit your changes (`git commit -m 'Add amazing feature'`)\r\n4. Push to the branch (`git push origin feature/amazing-feature`)\r\n5. Open a Pull Request\r\n\r\n---\r\n\r\n## License\r\n\r\nThis project is licensed under the MIT License - see the [LICENSE.txt](LICENSE.txt) file for details.\r\n\r\n---\r\n\r\n## Author\r\n\r\n**Your Name**\r\n- GitHub: [@Hammail-Riaz](https://github.com/Hammail-Riaz)\r\n- Email: hammailriaz.dev@gmail.com\r\n\r\n---\r\n\r\n## Changelog\r\n\r\n### Version 0.1.0 (Initial Release)\r\n- 2x2 and 3x3 matrix operations\r\n- Linear equation solver with multiple methods\r\n- Comprehensive error handling\r\n- Full documentation and examples\r\n\r\n---\r\n\r\n## Acknowledgments\r\n\r\n- Built with Python 3.8+\r\n- Inspired by linear algebra education needs\r\n- Thanks to all contributors\r\n\r\n---\r\n\r\n## Support\r\n\r\nIf you encounter any issues or have questions:\r\n- Open an issue on [GitHub Issues](https://github.com/yourusername/equations_solvers/issues)\r\n- Check the [documentation](#documentation)\r\n- Contact: hammailriaz.dev@gmail.com\r\n\r\n---\r\n\r\n**Made with \u2764\ufe0f for mathematics and Python enthusiasts**\r\n",
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