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201mt2soln

# 201mt2soln - B U Department of Mathematics Mrttli 201...

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B U Department of Mathematics Mrttli 201 IvIat.rixTlieory Date: 27 November 2008 Full Name 17:00-18:30 Math 201 Number Student ID Fal! 2008 Second Midterm IMPORTANT i. Write down your name and surname on top of each page. 2. The exam consists of 6 questions some of which have multiple parts. 3. Read each question carefully and put your answers neatly under the space provided. 4. Showall your work. Correct answers without justification will not get credit. 5. Calculators are not allowed. Q1 Q2 Q3 Q4 Q5 Q6 TOTAL 2G pt:; J 5 pt:-. 15 pt.s 15 pt.s 15 pts 100 pts 1.) [5 pt.s] a) Given a set of distinct noi1Zero vectors, define what it means for its elements to be Iiiicitriy iiidepeiident. \ ~;~ S - ':) "i "'. 7 be Q. -:X::.X-~ cU s\iC\C.:t (\:)T2-z'C' \J e:CTi>:-:S ........... , .\.- ~. - "\ 'i \ J .' 'i il:- ') -\~,-.'\n e.. e\. -(.f'!' ef'\-\s ~oS D..-c. ~\ (\ C:~.cr '.j \(") cl.. C.. ofJ E.- ,,:::.l::'-ov'-- \- .. 'or \- ~ \.:::\\] sc\.I...--\..-ho:"\-t-c CSZ{ \tt -\: _ .. -tCL \J\<. =0 'S> ci==O =-C2-' -=::Cic. III pi:,] b) Pro\'(·' ibal a set of nonzcro mutiially (i. e. pairwise) ortliogoiial vectors in Rii are liiiem-ly IJd(·ii(~lid(·iil.

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