Gaussian Elimination for Solving Linear Systems
Linear Systems & Numerical Methods DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Gaussian Elimination for Solving Linear Systems, Partial Pivoting, Backward Substitution, Upper Triangular Matrix, Elementary Row Operations, Pivot Element, Augmented Matrix, Floating-Point Precision, Numerical Analysis, Linear Algebra, Scientific Computing, Algorithm Design, Computational Mathematics, Direct Solvers for Linear Systems, Matrix Factorization Techniques, Numerical Stability Analysis, Algorithm Complexity Analysis, Floating-Point Computations.
Task: Implement the Gaussian Elimination Method Your task is to implement the Gaussian Elimination method, which transforms a system of linear equations into an upper triangular matrix. This method can then be used to solve for the variables using backward substitution. Write a function gaussian elimination(A, b) that performs Gaussian Elimination with partial pivoting to solve the system \(Ax = b\). The function should return the solution vector \(x\).