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### StA_verkefni_09_lausnir[1]

Course: ECONOMICS 102G, Spring 2011
School: Uni. Iceland
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Word Count: 1274

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slands Viskipta- Hskli og hagfrideild Viskiptaskor hausti 2009 Strfri A fyrir viskiptafringa. Heimadmi 9 1. Finni tmrk og segi hvers elis au eru: 3 a) z = x1 x1 x2 + x2 20 z1 = 1 x2 = 0 x2 = 1 x1 = 1 z2 = x1 + 3 x = 0 z11 = 0 z12 = 1 0 1 H = z21 = 1 z22 = 6 x2 1 6 2 2 H1 = 0, H 2 = 1 sulpunktur 3 b) z = x12 x1 x2 + x2 20 0 x2 = 0 z1 = 2 x1 x2 = 0 2 1 x2 = 2 x1 x1 + 12 x1 = 0...

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slands Viskipta- Hskli og hagfrideild Viskiptaskor hausti 2009 Strfri A fyrir viskiptafringa. Heimadmi 9 1. Finni tmrk og segi hvers elis au eru: 3 a) z = x1 x1 x2 + x2 20 z1 = 1 x2 = 0 x2 = 1 x1 = 1 z2 = x1 + 3 x = 0 z11 = 0 z12 = 1 0 1 H = z21 = 1 z22 = 6 x2 1 6 2 2 H1 = 0, H 2 = 1 sulpunktur 3 b) z = x12 x1 x2 + x2 20 0 x2 = 0 z1 = 2 x1 x2 = 0 2 1 x2 = 2 x1 x1 + 12 x1 = 0 x1 = 1 2 z2 = x1 + 3 x2 = 0 12 x2 = 6 ( 0, 0 ) ( x1 , x2 ) = 1 1 12 , 6 2 1 H ( 0, 0 ) = sulpunktur z11 = 2 z12 = 1 1 0 z21 = 1 z22 = 6 x2 1 1 2 1 H ,= min imum 12 6 1 1 Kennari: Gumundur lafsson lektor Sa 1 Hskli slands Viskipta- og hagfrideild 2. Viskiptaskor hausti 2009 Strfri A fyrir viskiptafringa. Gefnar eru frslurnar: 3 4 2 a = , b = , c = 3 31 4 a) Finni a-2b-5c og |a-2b-5c| 3 4 2 21 a-2b-5c = 2 5 = 3 31 4 85 21 = 212 + 852 = 87,56 |a-2b-5c| = 85 b) Finni horni milli a og b. 3 4 3 31 12 93 cos v = = = 0, 7934 v = cos 1 ( 0, 7934 ) = 142,5 9 + 9 12 + 961 3 4 3 31 3. Gefin eru eftirfarandi fylki: 3 8 A= 4 12 4 p= 6 c T = [ 2 5] 8 1 D= 3 2 6 x= 3 3 2 8 E= 1 6 10 1 2 5 G = 3 8 9 7 6 4 2 f = 1 Finni vddirnar: 3 8 A= 4 12 ( 2x2) 4 p= 6 ( 2X1) cT = [ 2 5] ( 1X2) 8 1 D= 3 2 ( 2 X 2 ) 6 x= 3 ( 2x1) 3 2 8 E= 1 6 10 ( 2x3) 1 2 5 G = 3 8 9 7 6 4 ( 3x3) 2 f = 1 ( 2 x1) og san ef hgt er: A+D xf D+E xp p+c EG pT + c D+A 3 8 8 1 11 9 A + D = + = 4 12 3 2 7 14 Kennari: Gumundur lafsson lektor Sa 2 Hskli slands Viskipta- og hagfrideild Viskiptaskor hausti 2009 Strfri A fyrir viskiptafringa. 6 2 8 x f = + = 3 1 4 2 4 6 p + c = + = 6 5 11 T p + c ekki hgt D+A=A+D D + E ekki hgt 6 4 2 x p = = 3 6 3 E G ekki hgt 4. Bylti fylkjunum dmi 8 (finni Transpose). 3 4 AT = 8 12 xT = [ 6 3] 5. 2 8 3 =c= DT = 5 1 2 3 1 1 3 7 2 6 GT = 2 8 6 f T = 2 1 T E = [] 8 10 5 9 4 p T = [ 4 6] (c ) TT Gefin eru tv lkn: a) Markaslkan q D = 10 0,2 p q S = 1 + 0,4 p b) Rekstrarlkan R = 10 + 5Q C = 100 + 3Q Leysi jfnukerfin me v a nota fylkjareikning (finni andhverfa fylki) og tlki niursturnar. Er hgt a gefa stulum andhverfanna einhverja merkingu. a) Markaslkan q D = 10 0,2 p q S = 1 + 0,4 p qD = 10 0, 2 p q + 0, 2 p = 10 1 0, 2 q 10 = qS = 1 + 0, 4 p q 0, 4 p = 1 1 0, 4 p 1 1 q 1 0, 2 10 1 0, 4 0, 2 10 1 3,8 6 1 3 = 1 = 0, 6 1 1 = 0, 6 11 = 18 1 1 p 1 0, 4 3 b) Rekstrarlkan R = 10 + 5Q C = 100 + 3Q Kennari: Gumundur lafsson lektor Sa 3 Hskli slands Viskipta- og hagfrideild Viskiptaskor hausti 2009 Strfri A fyrir viskiptafringa. R = 10 + 5Q R 5Q = 10 1 5 R 10 = R =C C = 100 + 3Q R 3Q = 100 1 3 Q 100 1 R 1 5 10 1 3 5 10 235 Q = 1 3 100 = 2 1 1 100 = 45 6. (Excel) Gefin eru eftirfarandi fylki: 8 7 y = 10 12 9 1 1 X = 1 1 1 6 3 8 9 4 Finni eftirfarandi fylki: XT XTy XTX (XTX)-1 XT 1 1 1 1 1 = 6 3 8 9 4 XTy 1 1 1 1 = 6 3 8 9 XTX 1 1 1 1 = 6 3 8 9 det(XTX) (XTX)-1XTy 8 7 1 46 10 = 4 293 12 9 1 6 1 3 5 30 1 1 8 = 4 30 206 1 9 1 4 1 5 30 1 206 30 (XTX)-1 = = 130 30 5 30 206 5 30 det(XTX)= = 130 30 206 686 1 206 30 46 130 = (XTX)-1XTy= 130 30 5 293 85 130 Kennari: Gumundur lafsson lektor Sa 4
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