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Math 314H Solutions to Homework # 1 1 Let = f1x;1x2;xx2g be a subset of P 2 (a) Prove that is a basis for P2 Let = f1;x;x2g be the standard basis for P2 and consider the linear transforma tion T P2!R3 de ned by T(f) = f , where f is the coordinate vector of f with respect to Now, is a basis for P2 if and only if T( ) =.

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How to decrypt code encoded with Jefferson's wheel cipher?. And more generally M(n)(0) = E(), n ≥ 1(8) The mgf uniquely determines a distribution in that no two distributions can have the same mgf So knowing a mgf characterizes the distribution in question. Have an infimum and a supremum Let uA and uB be the supremum of A and B respectively We want to show that uA uB = sup(A B) Let c be an arbitrary element of A B Then there exist a 2 A and b 2 B such that c = a b Now, c = ab • uAb • uAuB where the first inequality follows from uA = supA and the second follows from uB = supB This shows that uAuB is an upper bound for AB.

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The DFW CIV, DFW CV, DFW CVI, and DFW F37 were a family of German reconnaissance aircraft first used in 1916 in World War IThey were conventionally configured biplanes with unequalspan unstaggered wings and seating for the pilot and observer in tandem, open cockpits Like the DFW CII before them, these aircraft seated the gunner to the rear and armed him with a machine gun on a ring mount. 315 f g h ` _ k l \ h l j m ^ h \ _ i h t e Z j k d Z b k l h j b y g Z g _ f k d b b t e Z j k d b _ a b d K i h j _ ^ ^ h k l h \ _ j g b ^ Z g g b _ i h q. 122 Behavior of the Solutions 179 Example 126 Find the solution y y x of y 2y 5y 0, with the initial values y 0 2 y 0 1 The auxiliary equation r2 2r 5 0 has the solutions r.

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