linear algebra question

Problem:

Let matrix $A$ be a 2×2 matrix defined as follows:

A=(3421)A = begin{pmatrix} 3 & 4 \ 2 & 1 end{pmatrix}A=(3241)

Let $\mathbf{v}$ be a vector:

v=(13)mathbf{v} = begin{pmatrix} 1 \ 3 end{pmatrix}v=(13)

1. Find the matrix-vector product $A\mathbf{v}$.
2. Determine if the vector $\mathbf{v}$ is an eigenvector of the matrix $A$, and if so, find the corresponding eigenvalue.