here is sagemath m = matrix([[0, 1, 0], [0, 0, 1], [1, 0, 0]]) v = vector([2, 3, 1]) m \ v (1, 2, 3) and then

here is sagemath m = matrix([[0, 1, 0], [0, 0, 1], [1, 0, 0]]) v = vector([2, 3, 1]) m \ v (1, 2, 3) and then sol = m \ v m * sol (2, 3, 1)