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Ch.1 Solutions Pg13

# Ch.1 Solutions Pg13 - £16 3 ISM Linear Algebra Section 1.2...

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Unformatted text preview: £16. 3. ISM: Linear Algebra Section 1.2 must be positive as well, meaning that \$3 4:: 5—93. These oonstrajnts leave us with only one possibility, \$3 = 4, and we can compute the corresponding values :1 = 15 + £33 = 2U anderz=1?—%Ia=3. Thus, we have 2|] one—dollar bills, 8 ﬁve—dollar bills, and 4 ten—dollar bills. Let 11,32, 1:3 be the number of El] oent, 5D cent, and 2 Euro coins, respectively. Then we , _ 2:1 +32 +33 = 1001'] need solutlons tn the system. .231 +532 +233 =1mﬂl _ _5ﬂ this system reduces to: \$1 \$2 :3: _= saga} Our solutions are then of the form 1'2 = 431:3 + T . Unfortunately for the meter 1'3 1'3 maids, there are no integer solutions to this problem. If 1:; is an integer, then neither 31 nor 332 will he an integer, and no one will ever claim the Ferrari. 1.2 11—255 _,11—255—H_,1[1—1IJE13 sees-WI! DisE—s aisE—s m—lﬂz =13 1: =13+1ﬂz a: 13+lﬂt y = —S—St ,whererisanarbitrarjrrealnumher. z t 34—1Esmqlg—gig 41%—%E% s s —25 3 s s —25 3 430'} [1 It] :15 —13 This system has no solutions, since the last row represents the equation D = —13. 3:4—2y—33 yandzareﬁ‘eemiables;lety=sandz=t. 1r 4 — 25 — 3t 1: = s , where s and t are arbitrary real numbers. 2 r 13 ...
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