We have, $\mathrm{A}=\left[\begin{array}{ll}3 & 5\end{array}\right]_{1 \times 2}$ and $\mathrm{B}=\left[\begin{array}{ll}7 & 3\end{array}\right]_{1 \times 2}$
Let $C=\left[\begin{array}{l}x \\ y\end{array}\right]_{2 \times 1}$ is a non-zero matrix of order $2 \times 1$.
$$
\therefore A C=\left[\begin{array}{ll}
3 & 5
\end{array}\right]\left[\begin{array}{l}
x \\
y
\end{array}\right]=[3 x+5 y]
$$
and $\mathrm{BC}=\left[\begin{array}{ll}7 & 3\end{array}\right]\left[\begin{array}{l}x \\ \mathrm{y}\end{array}\right]=[7 x+3 \mathrm{y}]$
For $\mathrm{AC}=\mathrm{BC}$,
$$
[3 x+5 y]=[7 x+3 y]
$$
On using equality of matrix, we get
$$
3 x+5 y=7 x+3 y
$$
$$
\Rightarrow y=2 x \therefore C=\left[\begin{array}{c}
x \\
2 x
\end{array}\right]
$$