Math 54 - Quiz 05, Spring 2006

Math 54 - Quiz 05, Spring 2006 - f ( x ) dx for any f ∈ C...

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Math 54, Quiz 5 Sections 202/203 GSI Carter Name: 1. For each of the following statements, write the word “true” or “false.” (a) Let T 1 : U V and T 2 : V W be two linear transformations. Then the function S from U to W defined by S ( u ) = T 2 ( T 1 ( u )) for any u U is a linear transformation. (b) The function E : C [ a, b ] R given by E ( f ) = R b a x ·
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Unformatted text preview: f ( x ) dx for any f ∈ C [ a, b ] is a linear transformation. 2. Give the coordinates of the polynomial p ( x ) = 1-x + x 3 in terms of the basis { 1 , x-1 , ( x-1) 2 , ( x-1) 3 } of the vector space P 3 . Write your answer in the form of a column vector. 1...
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