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Unformatted text preview: independent. • If function is one of f 1 ,f 2 , ··· ,f n , then they linearly dependent. • Two nonzero functions f ( t ) and g ( t ) are linearly dependent over [a, b] if and only if f ( t ) = sg ( t ) for a constant s 6 = 0 and all a ≤ t ≤ b , for example, f ( t ) = t and g ( t ) = 4 t are linearly dependent but f ( t ) = t and g ( t ) = 4 t 2 are not, even f (0) = 4 g (0) and f (1) = 4 g (1) . • There are exists inﬁnite many functions that are linearly independent. For example the set { 1 ,t,t 2 ,t 3 , ··· ,t n , ···} is a linearly independent set....
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
 Spring '11
 Dr.Han

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