2649.sagews

# this matrix fails to be inverted (solved) in MATLAB or R
A=Matrix([[4,-2,5,-26],[1,-1,-2,5],[2,-1,3,-15],[-1,-2,1,-10]])
A

[ 4 -2 5 -26] [ 1 -1 -2 5] [ 2 -1 3 -15] [ -1 -2 1 -10]

kernel(A)

Free module of degree 4 and rank 1 over Integer Ring Echelon basis matrix: [ 20 -5 -37 1]

w = vector([0,-3,4,1])     # this vector solves for columns
w
k = vector([20,-5,-37,1])  # this one for rows
k * A

(0, 0, 0, 0)

w * A.transpose()

(0, 0, 0, 0)