(c) Use the LU method in the SciPy library (https://scipy.org) to determine the LU decomposition of the following matrices:
C =
[1 1 -3 -4
-2 2 4 4
2 -4 -1 -1
3 1 4 -3]
D =
[1 2 2 -4
4 1 -4 4
-4 -5 3 -4
1 1 -4 1
-2 2 -2 -4
3 2 -4 2]
(d) The inverse Q^(-1) of a matrix Q ∈ R^(n×n) may be computed as follows: Let x_1, x_2, ..., x_n ∈ R^n be the solutions of the n linear systems Qx_j = e_j, where j ∈ {1, 2, ..., n} and e_j is the jth element of the standard basis of R^n. Then Q^(-1) = [x_1 x_2 ... x_n]. Find the inverse of the matrices A, B, C, and D using this method, and each matrix's respective LU decompositions (that you previously computed). For the matrices A and B, the calculations must be done manually without any programming aid. For the matrices C and D, use the methods lu_factor and lu_solve from the SciPy library.
