Gaussian elimination converts the augmented matrix [A|b] to row-echelon form (REF) or reduced row-echelon form (RREF) using elementary row operations. Back-substitution then gives the solution.
What are real-world applications of Gaussian elimination?
Gaussian elimination is used in electrical circuit analysis (finding currents via Kirchhoff's laws), structural engineering (solving force equilibrium equations), computer graphics (transformations and lighting calculations), economics (input-output models), and virtually any engineering or science problem that requires solving simultaneous linear equations.
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