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Gaussian Elimination Solver

🔢 Gaussian Elimination Solver

Use this solver to solve a system of equations using the Gaussian Elimination method with step-by-step solutions.

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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 EquationsSolution
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.

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