Null Space Basis

Problem

Find a basis for the null space of matrix A (vectors x with A*x = 0).

Compute the RREF, then for each free column build a basis vector with a 1 in that free position and the negated RREF pivot entries elsewhere. Return the basis in free-column order; return [] if the null space is trivial.

Hint

Each free variable produces one basis vector; read its coordinates from the RREF.

Test cases

case 1

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

expected: [[-2,1]]

case 2

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

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

case 3

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

expected: []

case 4

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

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

Starter codePython

def null_space_basis(A):
    # Your code here
    pass

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