Prove the linear independence of $\{v_1,v_2+v_2 \}\,$? 
Prove that if $\{v_1,v_2\}$ are linearly independent (LI), then also $\{v_1,v_1+v_2\}$ are linearly independent.
Is the converse true?

I have proved the first part, but now i am stuck on whether the converse is true.
that is, if the $ \{ v_1,v_1+v_2 \} $ are LI, so are $\{v_1,v_2\}$.
How can i prove this?
Thanks in advance.

$\{v_1 ,v_1 +v_2 \}$ L.I $\implies \{v_1,v_2 \}$ L.I
Proof : Assume the contrary that $\{v_1,v_2 \}$  L.D
Then, $v_2 =\lambda v_1$ for some scalar $\lambda$
Then $v_1+ v_2 = (1+\lambda ) v_1$
And this implies $\{v_1 ,v_1 +v_2 \}$ is linearly dependent.
