Unformatted text preview: n ) . Now just observe that the right hand side is x · a f . This line of reasoning is just what we used to prove Theorem 2 in the ﬁrst place. 5.25 For any vector ± a b c ² , deﬁne the polynomial p ( x ) = a + bx + cx 2 . In turn, deﬁne the number R 1 p ( x )d x . Putting the pieces together, we get a function f from IR 3 to IR – we deﬁne f ³± a b c ²´ = Z 1 µ a + bx + cx 2 ¶ d x . (a) Show that f is a linear functional on IR 3 ; i.e., a linear transformation from IR 3 to IR . 21 /september/ 2005; 22:09 43...
View
Full Document
 Fall '08
 Gladue
 Calculus, Linear Algebra, Derivative, Vectors, Linear map, Tier One, Scaled Composites, Scaled Composites White Knight

Click to edit the document details