Given a matrix (as an np.array), return a vector as an np.array with shape (3,) in a way that depends on the injective, surjective, and bijective properties of .

If it is bijective, return a vector such that =(1,2,1).

If is not bijective because it is not injective, return a vector (that does not equal (1,1,1)) such that =(1,1,1).

If is not bijective because it is not surjective, return a vector v where the first two coordinate of are 1 and = for some vector . (E.g. = (1,1,z) for the correct value of .)

Note that for this problem will always either be surjective or injective.

Part A: A= np.array([[1,2,3],[2,1,1]])

Part B: A= np.array([[1,2],[3,4],[10,6]])

Part C: A= np.array([[1,2,3],[3,4,5],[4,10,6]])

(This is a linear algebra question meant to be solved on a Jupyter notebook using Python)