Inverse Function Theorem Jacobian

Problem

The inverse function theorem states that the Jacobian of the inverse map at a point is the inverse of the Jacobian at the corresponding point.

For J = [[a, b], [c, d]], return (1 / det) * [[d, -b], [-c, a]], or None when det = a*d - b*c == 0.

Hint

The inverse is the adjugate divided by the determinant; a zero determinant means no local inverse.

case 1

in: [1,0,0,1]

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

case 2

in: [2,1,1,1]

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

case 3

in: [1,2,3,4]

expected: [[-2,1],[1.5,-0.5]]

case 4

in: [2,4,1,2]

expected: null

Starter codePython

def inverse_jacobian(a, b, c, d):
    # Return the inverse 2x2 matrix, or None
    # Your code here
    pass

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