🔢 Gaussian Elimination Solver
| | ||||
| | ||||
| |
Example System:
2x + 3y – z = 5
4x – 2y + 3z = 6
-x + 5y + 2z = -4
Result will appear here…
📌 What is Gaussian Elimination?
Gaussian elimination is a method for solving systems of linear equations. It works by transforming the system into an upper triangular form, allowing easy back-substitution to find the solution.
📌 Applications of Gaussian Elimination
- Linear Algebra: Used to solve systems of equations.
- Engineering: Essential in circuit analysis and mechanics.
- Physics: Helps solve equations related to forces and motion.
- Computer Science: Used in algorithms for graphics and data processing.
📌 Example Calculations
System of Equations | Solution |
---|---|
2x + 3y – z = 5 4x – 2y + 3z = 6 -x + 5y + 2z = -4 | x = 1, y = -2, z = 3 |
❓ FAQs
Q1: What is the purpose of Gaussian Elimination?
✅ It simplifies a system of equations for easy solving.
Q2: Can Gaussian elimination be used for non-square matrices?
✅ Yes, it works for any system of linear equations.
Q3: What if a row has all zeros?
✅ This means the system may have infinite solutions or no solution.
Q4: What happens if a pivot is zero?
✅ Swap rows to avoid division by zero.
Q5: Is Gaussian Elimination the same as row echelon form?
✅ Yes, it transforms the matrix into upper triangular form.