Demonstrate that columns of the node–arc incidence matrix corresponding to arcs in each of the following cycles of the digraph in Exercise 10-1 form a linearly dependent set.

(a) (2, 5), (5, 2)

(b) (4, 2), (5, 2), (4, 5)

(c) (1, 2), (4, 2), (1, 4)

(d) (1, 4), (4, 5), (5, 3), (3, 1)