Economics Dynamics Problems 98

Economics Dynamics Problems 98 - 82 Economic Dynamics 9....

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82 Economic Dynamics per gram. If this charcoal was formed during the reign of Hammurabi, what is the likely time of Hammurabi’s succession? 9. (i) f 1 ( x ) and f 2 ( x ) are linearly dependent if and only if there exists con- stants b 1 and b 2 not all zero such that b 1 f 1 ( x ) + b 2 f 2 ( x ) = 0 for every x . Suppose b 1 ±= 0, then f 1 ( x ) =− ( b 2 / b 1 ) f 2 ( x ) and so f 1 ( x ) is a multiple of f 2 ( x ) and therefore the functions are linearly dependent. If the set of functions is not linearly dependent, then f 1 ( x ) and f 2 ( x ) are linearly independent. Show that y 1 = e rt and y 2 = te rt are linearly independent. (ii) f 1 ( x ), f 2 ( x ) and f 3 ( x ) are linearly dependent if and only if there exist constants b 1 , b 2 and b 3 not all zero such that b 1 f 1 ( x ) + b 2 f 2 ( x ) + b 3 f 3 ( x ) = 0 for every x . If the set of functions is not linearly dependent, then f 1 ( x ), f 2 ( x ) and f 3 ( x ) are linearly independent. Show that y 1 = e rt , y 2 = te rt and
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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