Rank-Nullity Count

Problem

Apply the rank-nullity theorem to a matrix A with n columns.

Compute the rank by Gauss-Jordan elimination and return [rank, n - rank], where n - rank is the nullity (dimension of the null space).

Hint

Count pivot columns during elimination; every column is either a pivot or a free variable.

case 1

in: [[[1,2],[3,6]]]

expected: [1,1]

case 2

in: [[[1,0],[0,1]]]

expected: [2,0]

case 3

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

expected: [0,2]

case 4

in: [[[1,2],[2,4],[0,1]]]

expected: [2,0]

case 5

in: [[[1,0,1],[0,1,1]]]

expected: [2,1]

Starter codePython

def rank_nullity(A):
    # Your code here
    pass

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