Answer and Step-by-step explanation:
A) False, take (1,-1) and (1,1) both in V, but the sum (2,0) is not
B) True, if A,B are symmetric then A+kB is symmetric as well for k scalar, and zero matrix is symmetric.
C) True. The zero polynom is in V and P+kQ verifies (P+kQ)(0)=P(0)+kQ(0)=0
D) True. zero is solution and f+kg is since all coefficients are linear.
E) True, same than C)
F) False , the zero function doesn't verify that ( and the closure for sum will fail anyway 4+4=8)
G) False, the zero function fail to satisfy this ODE
