Change of Basis Coordinates

Problem

Express vector v in the basis formed by the two vectors in basis = [b1, b2].

Return coordinates [c1, c2] such that v = c1*b1 + c2*b2. Return None if the basis vectors are linearly dependent.

Hint

Solve the 2x2 system whose columns are the basis vectors using the cross formula.

case 1

in: [[[1,0],[0,1]],[3,4]]

expected: [3,4]

case 2

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

expected: [1,1]

case 3

in: [[[2,0],[0,3]],[4,9]]

expected: [2,3]

case 4

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

expected: null

Starter codePython

def change_of_basis(basis, v):
    # Your code here
    pass

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