Answer
$\lambda=5$
Work Step by Step
If A is an nxn matrix, a scalar $\lambda$ is called an eigenvalue of A is there is a non-zero vector $v$ such that $Ax=\lambda x$. This vector is called the eigenvector of A corresponding to $\lambda$.
Hence here, we compute:
$Av=\begin{bmatrix}
3 &1 \\
4 & 2
\end{bmatrix}\cdot\begin{bmatrix}
1 \\
2
\end{bmatrix}=\begin{bmatrix}
5\\
10
\end{bmatrix}=5\begin{bmatrix}
1 \\
2
\end{bmatrix}=5v$
Thus we can see that $\lambda=5$.
