Linear Independence of t, e^t, sin(t) in Vector Space V

[hkus10]

Let V be the vector space of all real-valued continuous functions.
t, e^t, sin(t) are in V.
Is t, e^t, sin(t) in V linearly independent?
My answer is yes.
However, how can I prove it which is that which do I have to show or can I just say the def of linear independent?

 

[Dick]

Let V be the vector space of all real-valued continuous functions.
t, e^t, sin(t) are in V.
Is t, e^t, sin(t) in V linearly independent?
My answer is yes.
However, how can I prove it which is that which do I have to show or can I just say the def of linear independent?

You CAN just say 'def of linear independence'. But that would be a stupid thing to say. What IS the 'def of linear independence'? That's what you have to show.