Answer
See answer below
Work Step by Step
Let:
$A_1=\begin{bmatrix}
1 & 0\\
1 & 2
\end{bmatrix}$
$A_2=\begin{bmatrix}
-1 & 1\\
2 & 1
\end{bmatrix}$
$A_3=\begin{bmatrix}
2 & 1\\
5& 7
\end{bmatrix}$
We can see that $3A_1+A_2=3\begin{bmatrix}
1 & 0\\
1 & 2
\end{bmatrix}+\begin{bmatrix}
-1 & 1\\
2 & 1
\end{bmatrix}=\begin{bmatrix}
2 & 1\\
5 & 7
\end{bmatrix}=A_3$
Hence $\{ A_1,A_2,A_3 \}$ is a linearly dependent set in $M_2(R)$
