Answer each question by True or False. Justify your answer.
(1) True or False? The set V = {p ? P2: p (7) = 0, p’ (7) = 0}is a subspace of P2.
(2) True or False? The set of 2 by 2 matrices whose entries areeither all 0 or all nonzero is a subspace of the set of all 2 by 2matrices M2×2(R).
(3) True or False? The set of all functions in C([0, 1]) suchthat f(0) = f( 1 /3 ) = f( 2 /3 ) = f(1) = 0 is a subspace. Note:C([0, 1]) is the set of continuous functions on [0,1].
(4) True or False? For an m × n matrix A, the null space isalways a subspace of Rn.
(5) True or False? The set of all solutions to the ODE y’’ + 2y’0 +y = 3e^x forms a vector space.
(6) True or False? The ODE y’’ +2y’ +y = cos(e^x ?7)+ sec(x) canbe solved using the technique of undetermined coefficients.
