mathematics

Question

plz someone explain.........

Comments

Draw graph from given matrix and match option form i to j no. of path of length 3 .

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and it's not tough to find $A^3$ directly.

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suppose a,b,c,d are 4 sequence of vertises of above matrix then no. of path of length 3 from vertex b to c is 3 here(b-b-b-c , b-c-c-c , b-c-d-c)

i have doubt as path (b-b-b-c) & (b-c-c-c) are same path or different.

Answer 1

	1	2	3	4
1	1	0	0	1
2	1	0	2	2
3	1	0	1	1
4	0	0	1	1

Number in Bold are elements of A³

So there exist only 1 path for V₁ to V₁

Similary  1 path from V₁ to V₄

2 path from V₂ to V₃ and so on

and each of these path has lenght 3 because of A³

^{Here is how A will look}