Let V = C ([a, b|) be the vector space consisting of all functions f(t) which are defined and continuous on the interval 0 ‰¤ t ‰¤ 1. Which of the following conditions define subspaces of V? Explain your answer.
(a) f(0) = 0
(b) f(0) = 2/(l)
(c) f(0)f(l)= 1
(d) f(0) = 0 or f(l) = 0
(e) f(I - r) = tf(t)
(f) f(1-t)=l- f(t)
(g)

(h)

(i)

Transcribed Image Text:

f(1)=I f(t)dt (t-1)f(r)dt = 0 f (s) sin s ds = sin t .