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# ps6 - Atsushi Inoue ECG 765 Mathematical Methods for...

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Atsushi Inoue ECG 765: Mathematical Methods for Economics Fall 2009 Problem Set ] 6 Due in class on Tuesday, October 13 1. Let A = a 11 a 12 · · · a 1 n a 21 a 22 · · · a 2 n . . . . . . . . . a m 1 a m 2 · · · a mn , x = b 1 b 2 . . . b n . Write Ax using a ij , b j and the Σ notation. (1 point) 2. Let f : X → < where X is an open set in < n . We say that f is homogeneous of degree p over X if f ( λ x ) = λ p f ( x ) for every λ and for every x X for which λx X . If such a function is differentiable at x , show that < x , f ( x ) > = pf ( x ) . (2 points) 3. Consider the following function f ( x, y ) = ( xy x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) Compute the partial derivatives f x and f y when ( x, y ) 6
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