Question

DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.

Answer 1

solution : where Given set w wat: f = -), V=C[V] f, g. EW functions of w flo) = -1 g (0) = -1 Let be any two Then and Now -2 (f+q) (0) front glo +4) t-1 ire. (f+g) & Wine ftg does not Wis no a subspace of u because it is not cloed under addition, belongs tow. Hence B Let f EU and be h EC [-1,1] =V If (o)=-1 any h (-1) function Then Now (h f) Co) h (f(o)) # -1 Hence (hf) (0) h (-1) #1 (hf) does not belongs to w. Hance W is not Entspace of because it is not closed under scalari multiplication option are true Hence 2 and (3 Ans)