midterm1sol

midterm1sol - Math 115a Lecture 3 Winter 2009 Midterm 1...

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Math 115a Midterm 1 Lecture 3 Winter 2009 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise, you may use without proof anything proven in the sections of the book covered by this test (excluding the exercises). Give complete, convincing, and clear answers (or points will be deducted). No calculators, books, or notes are allowed. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Question Points Score 1 10 2 10 3 10 4 10 Total: 40
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1. (a) (5 points) Let V be the set R 2 with the usual vector addition operation ( x 1 ,y 1 ) + ( x 2 ,y 2 ) = ( x 1 + x 2 ,y 1 + y 2 ) and with the scalar multiplication operation c ( x 1 ,x 2 ) = ( cx 1 ,x 2 ) . Is V a vector space over R ? Justify your answer using only the definition of a vector space (i.e. do not use anything that is proven in the book). Solution: By definition, a vector space must satisfy ( c 1 + c 2 ) v = c 1 v + c 2 v for every c 1 ,c 2 F and v V. However with the operations above (0 + 0)(1
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This note was uploaded on 01/27/2010 for the course MATH 7330 taught by Professor Davidson,m during the Spring '08 term at LSU.

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midterm1sol - Math 115a Lecture 3 Winter 2009 Midterm 1...

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