Span Membership 3D

Problem

Decide whether a vector v lies in the span of a list of 3D vectors.

Build the augmented matrix with the spanning vectors as columns and v as the last column, then row reduce. Return False if an inconsistent row (all zeros except the last entry) appears, and True otherwise.

Hint

v is in the span exactly when the augmented system is consistent.

Test cases

case 1

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

expected: false

case 2

in: [[[1,1,0],[0,0,1]],[2,2,5]]

expected: true

case 3

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

expected: false

case 4

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

expected: true

case 5

in: [[[1,2,3],[2,4,6]],[3,6,9]]

expected: true

Starter codePython

def span_membership_3d(vectors, v):
    # Your code here
    pass

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