f3(x) = 1/2(f1(x) - f2(x)) so we know that f3(x) is linearly dependent on f1,f2.Let S be the vector space consisting of the set of all linear combinations of the functions
f1(x)= e^(x)
f2(x)= e^(-x)
f3(x)= sinh(x)
Determine a basis for S, and hence, find dim[S].
Now, we consider f1(x),f2(x)
c1*f1(x) + c2*f2(x) = 0
c1 = c2 = 0. f1 and f2 are Linearly independent and are a basis. Dim[S] = 2.
Is my answer correct?
Thanks