To find the matrix-vector product Av, we multiply the elements of each row of A by the corresponding elements of v and then sum the products:

Av = (3 * 1 + 4 * 3)
     (2 * 1 + 1 * 3)
   = (15)
     (5)

To determine if v is an eigenvector of A, we need to check if Av is a scalar multiple of v. In other words, we need to see if there exists a scalar λ such that:

Av = λv

In this case, we have:

(15) = λ(1) (5) = λ(3)

From the second equation, we get:

λ = 5/3

Substituting this value into the first equation, we get:

15 = (5/3)(1)

This is true, so v is indeed an eigenvector of A with the corresponding eigenvalue λ = 5/3.