is linearly dependent if there exist some scalars ,not all 0, such that

Now, assume there exist some scalars . Recall that for some . If , we are done. Assume .

Rewriting the equation, we get:

.

So, if we choose, say, , then we'll choose , and now we have , not all 0, such that and thus Y is linearly dependent.

Can you follow on the second part from here?