Evaluating numerical algorithm
Gaussian Elimination is the foundational direct method for solving systems of linear equations . It transforms an augmented matrix into upper triangular form via row operations, then solves via back substitution. With partial pivoting, it handles near-zero pivots stably.
Repeat for each pivot column until upper triangular form is achieved.
Solve the 3×3 system:
Verify: — use the demo below with exact numbers to verify.
The calculator below shows every row reduction step live. It swaps rows when a pivot is 0, as in the textbook; switch on partial pivoting to always bring the largest pivot up, which keeps rounding errors small.
💡 Yellow column = constants vector b. Coefficient matrix A is on the left. Full system: Ax = b.