Reduced Row Echelon Form (RREF) Function
Linear Systems & Numerical Methods DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Implement Reduced Row Echelon Form (RREF) Function, Pivot Element, Row Swapping, Row Scaling, Row Replacement, Rank of a Matrix, Free Variables, Augmented Matrix, Linear Algebra, Numerical Methods, Algorithm Design & Analysis, Scientific Computing, Computational Mathematics, Matrix Transformations, Linear Systems Solving, Pivoting Strategies, Elementary Row Operations, Computational Complexity Analysis, Numerical Stability.
In this problem, your task is to implement a function that converts a given matrix into its Reduced Row Echelon Form (RREF). The RREF of a matrix is a special form where each leading entry in a row is 1, and all other elements in the column containing the leading 1 are zeros, except for the leading 1 itself. However, there are some additional details to keep in mind: Diagonal entries can be 0 if the matrix is reducible (i.e., the row corresponding to that position can be eliminated entirely). Some rows may consist entirely of zeros. If a column contains a pivot (a leading 1), all other entries in that column should be zero. Your task is to implement the RREF algorithm, which must handle these cases and convert any given matrix into its RREF.