Linear Algebra : Introduction To Linear Algebra PSET : https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/assignments/

25.py

import numpy as np
from scipy import linalg
from __future__ import print_function

K = linalg.toeplitz([-2, 1, 0, 0, 0, 0])

P, L, U = linalg.lu(K)

print (linalg.inv(L))

## Output:
#[[ 1.          0.          0.          0.         -0.         -0.        ]
# [ 0.5         1.          0.          0.         -0.         -0.        ]
# [ 0.33333333  0.66666667  1.          0.         -0.         -0.        ]
# [ 0.25        0.5         0.75        1.         -0.         -0.        ]
# [ 0.2         0.4         0.6         0.8         1.         -0.        ]
# [ 0.16666667  0.33333333  0.5         0.66666667  0.83333333  1.        ]]

26.py

from __future__ import print_function

import numpy as np
from scipy import linalg

SevenKInv = np.array([
        [6, 5, 4, 3, 2, 1],
        [5, 10, 8, 6, 4, 2],
        [4, 8, 12, 9, 6, 3],
        [3, 6, 9, 12, 8, 4],
        [2, 4, 6, 8, 10, 5],
        [1, 2, 3, 4, 5, 6]
    ])

K = linalg.toeplitz(np.array([2, -1, 0, 0, 0, 0]))

print (SevenKInv.dot(K))

"""
Output:
[[7 0 0 0 0 0]
 [0 7 0 0 0 0]
 [0 0 7 0 0 0]
 [0 0 0 7 0 0]
 [0 0 0 0 7 0]
 [0 0 0 0 0 7]]
"""