Unformatted text preview: A h corresponding to h , as in Theorem 2. SOLUTION (a) We use the deﬁnition of linearity, given in Section 2.2: Since f and g are linear, for any numbers a and b , and any x and y in IR n , f ( a x + b y ) = af ( x ) = bf ( y ) and g ( a x + b y ) = ag ( x ) = bg ( y ) . Therefore, h ( a x ) = ³ f ( a x + b y )) g ( a x + b y )) ´ = ³ af ( x ) = bf ( y ) ag ( x ) = bg ( y ) ´ = a ³ f ( x ) g ( x ) ´ + b ³ f ( y ) g ( y ) ´ = ah ( x ) + bh ( y ) . Thus, h is linear. (b) The matrix is ³ 1 2 3 3 2 1 ´ . Section 6 21 /september/ 2005; 22:09 44...
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 Fall '08
 Gladue
 Calculus, Linear Algebra, Derivative, Linear map, IR3

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