Minimum Norm Solution 2x3

Problem

Solve the underdetermined system A*x = b with A of shape 2x3 and linearly independent rows.

The minimum-norm solution is x = A^T (A A^T)^(-1) b. Return None if A A^T is singular.

Hint

The row-space formula picks the solution orthogonal to the null space, which is the shortest one.

case 1

in: [[[1,0,0],[0,1,0]],[2,3]]

expected: [2,3,0]

case 2

in: [[[1,1,1],[1,-1,0]],[3,0]]

expected: [1,1,1]

case 3

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

expected: [0.3333333333333333,0.3333333333333333,0.6666666666666666]

case 4

in: [[[1,2,3],[2,4,6]],[1,2]]

expected: null

case 5

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

expected: [0,0,0]

Starter codePython

def minimum_norm_solution(A, b):
    # Your code here
    pass

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