A = [ 1 2 1 -1 1
      1 0 1 -1 0
      1 2 1  0 0
      1 1 0  0 0
     -1 0 0  0 0]

Ainv = inv(A)

b = [0
     0
     0
     0
     1];

x = Ainv*b

A = [1  4  1
     1  2 -1
     3 14  6];

R = [ -13  5    3
      4.5 -1.5 -1
      -4   1    1];

A*R

inv(A)

U = [1 1 -1
     0 1 2
     0 0 1];
L = [1 0 0
    -1 1 0
    -2 1 1];
B = [1 2 3
     3 2 1
     1 0 1];
A = U*(B\L);
inv(A) 

A = Tridiagonal(randn(4), randn(5), randn(4))

inv(A)

L, U = lu(A, Val{false})
display(L)
display(U)