2025A3_09

# 2025A3_09 - -2 3(1 1-3 = b Are the vectors(1-1 1 and(1 1 1...

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MATH 2025 Fall 2009 Assignment 3, due Thursday, Nov. 5, 2009, before class For partial credit, show all your work! 1[12P]) Which one of the following deﬁnes an inner product on the given vector space V . If it is not an inner product list at least one condition from the deﬁnition that does not work and show why it does not work! a) V = R 2 , (( x,y ) , ( u,v )) = xv . b) V = R 3 , (( x,y,z ) , ( u,v,w )) = 2 xu + 4 yv + zw . c) V = R 3 , (( x,y,z ) , ( u,v,w )) = 3 xu - 2 yv + 10 zw . d) V = C ([ - 1 , 1]) (the space of continuous real valued functions on [ - 1 , 1]), ( f,g ) = R 1 - 1 f ( t ) g ( t ) e t dt . e) V = C ([ - 1 , 1]), R 1 - 1 f ( t ) g ( t ) tdt . g) V = C ([ - 1 , 1]), ( f,g ) = R 1 0 f ( t ) g ( t ) dt . 2[6P]) Consider the inner product (( x,y,z ) , ( u,v,w )) = 2 xu + 5 yv + 3 zw on R 3 : a) Evaluate ((1
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Unformatted text preview: ,-2 , 3) , (1 , 1 ,-3)) = b) Are the vectors (1 ,-1 , 1) and (1 , 1 , 1) orthogonal with respect to this inner product? 3[6P]) Evaluate the following inner product and norms using the inner product ( f,f ) = R 1-1 f ( t ) g ( t ) dt on C ([-1 , 1]): a) ( t 3 + 2 t 2-t,t 2 ) = b) k t 3-t k =. 4[6P]) Consider the inner product (( x,y,z ) , ( u,v,w )) = x ¯ u + y ¯ v + z ¯ w on C 3 . a) Evaluate the inner product ((1 + i, 2-3 i, 3) , (2 i, 2 + 3 i, 1)) = b) Evaluate the norm k (2 + i, 3-2 i,i ) k =....
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## This note was uploaded on 11/23/2011 for the course MATH 2025 taught by Professor Staff during the Spring '08 term at LSU.

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