Answer each question by True or False. Justify your answer. (1) True or False? The set...

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 are either all 0 or all nonzero is a subspace of the set of all 2 by 2 matrices M2×2(R).

(3) True or False? The set of all functions in C([0, 1]) such that 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 is always 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) can be solved using the technique of undetermined coefficients.

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Colby Messinger answered 1 year ago

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