2.15 pts.] By computing elements of the 4 th rows of appropriate powers of a suitable matrix, or otherwise, find and write down the answers to the following 5 questions about the graph on the right. (You can do computations on the opposite/facing page.)\ (i) How many paths of length 2 are there from vertex

d

to vertex

a

? Circle the answer\ (a) 3\ (b) 4\ (c) 6\ (d) 7\ (e) 8\ (ii) How many paths of length 2 are there from vertex

d

to vertex

b

? Circle the answel\ (a) 3\ (b) 4\ (c) 6\ (d) 7\ (e) 8\ (iii) How many paths of length 4 are there from vertex

d

to vertex

b

? Circle the answer.\ (a) 25\ (b) 43\ (c) 54\ (d) 78\ (e) 89\ (iv) How many paths of length 4 are there from vertex

d

to vertex

c

? Circle the answer.\ (a) 25\ (b) 43\ (c) 54\ (d) 78\ (e) 89\ (v) How many paths of length 4 are there from vertex

d

to vertex

d

? Circle the answer.\ (a) 25\ (b) 43\ (c) 54\ (d) 78\ (e) 89\ Page 2 of 6

2.15 pts.] By computing elements of the 4th rows of appropriate powers of a suitable matrix, or otherwise, find and write down the answers to the following 5 questions about the graph on the right. (You can do computations on the opposite/facing page.) (i) How many paths of length 2 are there from vertex d to vertex a ? Circle the answ (a) 3 (b) 4 (c) 6 (d) 7 (e) 8 (ii) How many paths of length 2 are there from vertex d to vertex b ? Circle the answ (a) 3 (b) 4 (c) 6 (d) 7 (e) 8 (iii) How many paths of length 4 are there from vertex d to vertex b ? Circle the answer. (a) 25 (b) 43 (c) 54 (d) 78 (e) 89 (iv) How many paths of length 4 are there from vertex d to vertex c ? Circle the answer. (a) 25 (b) 43 (c) 54 (d) 78 (e) 89 (v) How many paths of length 4 are there from vertex d to vertex d ? Circle the answer. (a) 25 (b) 43 (c) 54 (d) 78 (e) 89