Reduced Row Echelon Form

Problem

Transform matrix A into reduced row echelon form (RREF) using Gauss-Jordan elimination.

Each pivot is normalized to 1 and is the only nonzero entry in its column. Treat entries smaller than 1e-12 as zero. Return the result as a matrix of floats.

Hint

Normalize the pivot row, then clear the pivot column in every other row.

Test cases

case 1

in: [[[1,2],[3,4]]]

expected: [[1,0],[0,1]]

case 2

in: [[[1,2],[2,4]]]

expected: [[1,2],[0,0]]

case 3

in: [[[1,2,3],[4,5,6],[7,8,9]]]

expected: [[1,0,-1],[0,1,2],[0,0,0]]

case 4

in: [[[0,0],[0,0]]]

expected: [[0,0],[0,0]]

Starter codePython

def rref(A):
    # Your code here
    pass

4 test cases · run your code against them in the editor