The function that is useful in factorizing a matrix into a lower and upper triangular matrix is available in scipy.linalg as the lu function. 

In order to understand how LU factorization works, let us go through the following code snippets: 

1. Define a matrix:

A = np.array([[2., 1., 1.], [1., 3., 2.], [1., 0., 0.]]) 

2. Import relevant classes and packages:

import scipy.linalg as linalg 

3. Calculate the LU matrices using the lu function in scipy.linalg:

P, L, U = scipy.linalg.lu(A) 

4. Check the output of L:

print(L)
[[ 1.   0.   0. ] [ 0.5  1.   0. ] [ 0.5 -0.2  1. ]] 

5. Check the output of Uprint(U):

[[ 2.   1.   1. ] [ 0.   2.5  1.5] [ 0.   0.  -0.2]]

Note that, in the preceding outputs, L is a lower triangular matrix (all the elements in the upper half of the matrix are 0) and U is an upper triangular matrix. 

Once we obtain the L and U matrices, let us cross-check if the matrix multiplication of the two results in the input matrix A.

The matrix multiplication of L, U is as follows:

np.dot(L,U) 
[[  2.00000000e+00   1.00000000e+00   1.00000000e+00]
[  1.00000000e+00   3.00000000e+00   2.00000000e+00]
[  1.00000000e+00  -2.77555756e-17   0.00000000e+00]] 

In the preceding output, we notice that it is the same as the input matrix A, which we created earlier.