Linear Independence

[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?

[DrRocket]

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 need to use the definition of linear dependence and prove your assertion.