20f-sp96-rothschild-final

# 20f-sp96-rothschild-final - Name Mathematics 20F Final...

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Name : Time section meets: Mathematics 20F Professor Linda Rothschild June 13, 1996 Final Exam-Version A Instructions: Answer all questions. Use calculators for computation whenever it is quicker. There is not enough time to do all problems by hand. Indicate what the calculator has shown. Show some work or reason for each answer. For justiﬁcation, you can mention any fact cited in the text, but you cannot cite something shown in a homework problem. There are two versions of this exam; anyone who gives some answers corresponding to the other version will receive a 0 for the ﬁnal. 1. & 2. 20 3. & 4. 23 5. 30 4. 18 6. 12 7. & 8. 17 9. 30 10. 7 11. 12 12. 25 13. 12 14. 12 Total 200 Have a great summer! Typeset by A M S -T E X

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1. (10 pts.) Find the general solution of the system x 1 +5 x 3 +6 x 4 =6 x 1 + x 2 +2 x 4 =1 3 x 1 x 2 x 3 +11 x 4 =11 , 2. (10 pts.) A linear transformation T : R 4 R 4 is deﬁned by T ( x 1 x 2 x 3 x 4 )= x 1 x 2 + x 3 x 2 - x 3 x 1 +3 x 2 x 3 + x 4 . (a) Find the standard matrix for T . (b) Find a basis for the kernel of T .
(15 pts.) For A = 22 4 5 0 02 2 1 3 11 3 4 2 551 11 42 , ﬁnd the following. (a) rank of A (b) a basis for the row space of A (c) a basis for all b R 4 for which Ax = b has a solution.

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## This note was uploaded on 04/28/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.

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20f-sp96-rothschild-final - Name Mathematics 20F Final...

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