math110-fa2015-mt1-Holtz-exam - MATH 110 Fall 2015 midterm...

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Elementary Linear Algebra
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Chapter 4 / Exercise 15
Elementary Linear Algebra
Larson
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MATH 110, Fall 2015, midterm test #1. Name : Student ID # : GSI name : Discussion meeting time : Problem 1 Problem 2 Problem 3 Problem 4 Total All the necessary work to justify an answer and all the necessary steps of a proof must be shown clearly to obtain full credit. Partial credit may be given but only for significant progress towards a solution. Show all relevant work in logical sequence and indicate all answers clearly. Cross out all work you do not wish considered. Books and notes are allowed. Electronic devices are not allowed during the test. 1. (10pp.) Consider the linear map T : P 2 (IR) IR 3 : f 7→ ( f ( - 1) , f (0) , f (1)). Determine the dimensions of null T and range T . Is T invertible?
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Elementary Linear Algebra
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Chapter 4 / Exercise 15
Elementary Linear Algebra
Larson
Expert Verified
2. (10pp.) Let U := { f ∈ P 3 (IR) : f (1) = 0 } and W := { f ∈ P 3 (IR) : f 0 (1) = 0 } . Choose a basis for U W and extend it in two ways: to a basis of U and to a basis of

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