If $M, N$ are finite dimensional vector spaces with same dimension, then if $M$ is subset of $N$, then $M=N$. If $M, N$ are finite dimensional vector spaces with same dimension, then if $M$ is subset of $N$, then $M=N$.
I think i need to show that both vector spaces are spanned by the same bases in order to do this or to prove $N$ is subset of $M$? 
But i am not sure how to do this. 
Thanks

Hint:
Let $\;B:=\{m_1,...,m_k\}\;$ be a basis of $\;M\;$ . Then $\;B\;$ is a linearly independent set of $\;N\;$ as $\;M\le N\;$ . But we're also given $\;k=\dim M=\dim N\;$ , so...complete here.
