Unformatted text preview: is a magic square with magic constant 34. (This matrix appears in D¨urer’s Melencolia I .) Prove that the set of 3 × 3 magic squares is a vector space of dimension 3. 2. [4 marks] Given a polynomial p ( x ), let p ( i ) ( x ) denote its i th derivative. Let p ( x ) be a polynomial of degree n . Prove that B = ± p ( x ) , p (1) ( x ) , . . . , p ( n ) ( x ) ² is a basis for P n . Suppose p ( x ) = x n . Let S = ± x n , x n1 , . . . , x, 1 ² denote the standard basis for P n . Find the changeofcoordinates matrices from B to S and from S to B ....
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 Spring '09
 FokShuen
 Linear Algebra, Algebra, Addition, Derivative, Vector Space, Euclidean vector

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