- #1
Nexttime35
- 46
- 1
Homework Statement
Is the following set linearly dependent or independent? And does this set span the given space?
{eX, e-x}[itex]\in[/itex]C∞(R)
Homework Equations
The Attempt at a Solution
So, if it's linearly independent, then:
k1ex +k2e-x = 0 where k1,k2=0 and only 0. But if you let k1= -1/(e^x) and k2 = 1, then you also get 0, so this set is linearly dependent. I believe I am correct with this logic.
Now how do I go about checking whether the set is in the span of the vector space?