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115A_practice_midterm1

# 115A_practice_midterm1 - Practice Midterm 1 Problem 1 Let V...

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Practice Midterm 1

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Problem 1. Let V = { ( a 1 , a 2 ) : a 1 , a 2 IR } . Define addition of elements of V coordinatewise, and for ( a 1 , a 2 ) in V and c IR, define c ( a 1 , a 2 ) = (0 , 0) , if c = 0 ( ca 1 , a 2 c ) , if c 6 = 0 Is V a vector space over IR with these operations? Justify your answer. 2
Problem 2. Determine whether the following set W = { ( a 1 , a 2 , a 3 ) R 3 : 2 a 1 - 7 a 2 + a 3 = 0 } is a subspace of IR 3 under the coordinatewise addition and scalar multipli- cation defined on IR 3 . 3

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Problem 3. Determine whether the vector (2 , - 1 , 1) is the span of S = { (1 , 0 , 2) , ( - 1 , 1 , 1) } .

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115A_practice_midterm1 - Practice Midterm 1 Problem 1 Let V...

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