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a-cl-prereq-linc - Linear Algebra MAS4105 3247 Practice-A...

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Linear Algebra MAS4105 3247 Practice-A Prof. JLF King 23Aug2011 Welcome: This is a practice prereq exam. We’ll have the actual prereq exam ( which will be shorter ) , in class, on Wedn, 25Aug2010 . Please bring lined-paper for the short induction proof. The prereq counts only 4% 8% of the course grade. It’s purposeisforyouto self-evaluate ifyouhavetheprerequisite knowledge for the Theoretical Linear Algebra course. If you’ve forgotten a little, that’s fine, but if you are shaky on a lot of material, then you should consider using this semester to review, and taking the Theoretical course in Spring. A1: On your own sheets of paper, please write ( double- spaced ) proofs of the following, in complete English sen- tences. Do not restate the problem. Bin1 Define binary operation “ ”, on pair of reals, by x y := xy + y . Prove or disprove ( i.e give an explicit coun- terexample ): “ ” is associative. On the set of postive real numbers, define “ F ”, a binary operation, by a F b := a log( b ) . Prove or disprove: “ F ” is associative.
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