I previously had to prove the statement, and I did so by showing there were scalars a and b that were equal to each other but now I have to give a counterexample. I just proved this hypothesis' correctness, did I prove it wrong or is there a proper counterexample?

For reference, I proved the hypothesis like this:
Given vector w $\in$ Span($v\_1, v\_2, v\_3$), we have $a\_1v\_1 + a\_2v\_2 + a\_3v\_3$ = w and $b\_1v\_1 + b\_2v\_2 + b\_3c\_3$ = w
With some basic algebra, we can reach the point where $a\_1-b\_1=a\_2-b\_2=a\_3-b\_3=0$