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3. In each of the following problems, decide whether the given subset W of the vector space V is or is not a subspace of V. If not,

identify at least one requirement that is not satisfied. Assume that the standard definitions of addition

and scalar multiplication

hold.

(a) V = P2, W = {p(t) | degree of p(t) = 2}

W = = {ƒ(t) | ƒ(0) = f(1) =

W= {f(t) | ƒ" +2f = 4}

= { x = R₁ |

(b) V = C[0, 1],

(c) V = C² [0, 1],

(d) V = R", W =

ht

€ R¹ | AX = Ú, where A € Mmn, ↳ ‡ ¯}

Boul

Fig: 1