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%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300dpi
TeXDict begin
%%PaperSize: a4

%%EndSetup
%%Page: 1 1
1 0 bop 60 203 a Ff(Mathematisc)n(hes)17 b(Institut)750
b(WS)19 b(2000/2001)60 264 y(der)f(Univ)n(ersit)385 266
y(\177)385 264 y(at)g(M)507 266 y(\177)505 264 y(unc)n(hen)919
b(Blatt)18 b(1)60 324 y(Prof.)h(Dr.)f(B.)g(P)n(areigis)250
620 y Fe(Lineare)24 b(Algebra)e(und)i(analytisc)n(he)f(Geometrie)g(I)
120 734 y Fd(1.)h(Seien)13 b Fc(A)h Fd(und)h Fc(B)h Fd(zw)o(ei)d
(Mengen.)h(Zeigen)f(Sie)h(folgende)g(Bezieh)o(ung)e(f)1472
736 y(\177)1471 734 y(ur)j(die)e(P)o(otenz-)182 795 y(mengen:)697
855 y Fb(P)t Fd(\()p Fc(A)d Fb(\\)h Fc(B)s Fd(\))j(=)f
Fb(P)t Fd(\()p Fc(A)p Fd(\))e Fb(\\)g(P)t Fd(\()p Fc(B)s
Fd(\))1708 942 y(\(5\))120 1044 y(2.)24 b(Seien)17 b
Fc(\032)f Fd(=)g(\()p Fc(A;)8 b(B)s(;)g(U)d Fd(\),)16
b Fc(\033)i Fd(=)e(\()p Fc(B)s(;)8 b(C)q(;)g(V)i Fd(\))18
b(und)g Fc(\034)k Fd(=)16 b(\()p Fc(C)q(;)8 b(D)q(;)g(W)f
Fd(\))17 b(Relationen.)g(Zeigen)182 1104 y(Sie,)e(da\031)824
1164 y(\()p Fc(\034)6 b(\033)r Fd(\))p Fc(\032)13 b Fd(=)h
Fc(\034)6 b Fd(\()p Fc(\033)r(\032)p Fd(\))182 1251 y(gilt.)1441
b(\(5\))120 1353 y(3.)24 b(Wir)16 b(b)q(etrac)o(h)o(ten)h(ein)f
(Quadrat,)h(dessen)g(Ec)o(kpunkte)f(im)f(Uhrzeigersinn)h(mit)f
Fc(a)p Fd(,)h Fc(b)p Fd(,)182 1413 y Fc(c)22 b Fd(und)f
Fc(d)h Fd(b)q(ezeic)o(hnet)e(sind,)h(und)h(de\014nieren)f(zw)o(ei)f
(Symmetrie)o(n)f Fc(\033)1489 1420 y Fa(1)1530 1413 y
Fd(und)j Fc(\033)1661 1420 y Fa(2)1702 1413 y Fd(des)182
1473 y(Quadrates)17 b(durc)o(h)f(die)f(F)l(orderung)728
1583 y Fc(\033)756 1590 y Fa(1)775 1583 y Fd(\()p Fc(a)p
Fd(\))e(=)h Fc(a)97 b(\033)1055 1590 y Fa(1)1075 1583
y Fd(\()p Fc(b)p Fd(\))13 b(=)h Fc(d)182 1693 y Fd(bzw.)732
1753 y Fc(\033)760 1760 y Fa(2)780 1753 y Fd(\()p Fc(a)p
Fd(\))f(=)h Fc(c)97 b(\033)1055 1760 y Fa(2)1075 1753
y Fd(\()p Fc(b)p Fd(\))13 b(=)h Fc(b)203 1855 y Fd(\(a\))24
b(Erkl)381 1857 y(\177)381 1855 y(aren)d(Sie,)e(w)o(arum)h(auc)o(h)g
Fc(\033)903 1862 y Fa(1)923 1855 y Fd(\()p Fc(c)p Fd(\))h(=)g
Fc(c)g Fd(und)g Fc(\033)1234 1862 y Fa(1)1254 1855 y
Fd(\()p Fc(d)p Fd(\))g(=)h Fc(b)e Fd(bzw.)g Fc(\033)1585
1862 y Fa(2)1605 1855 y Fd(\()p Fc(c)p Fd(\))h(=)g Fc(a)289
1915 y Fd(und)c Fc(\033)415 1922 y Fa(2)434 1915 y Fd(\()p
Fc(d)p Fd(\))d(=)g Fc(d)j Fd(gelten)e(m)o(u\031.)200
1996 y(\(b\))24 b(Zeigen)16 b(Sie,)f(da\031)i Fc(\033)656
2003 y Fa(1)686 1996 y Fb(\016)11 b Fc(\033)750 2003
y Fa(2)784 1996 y Fd(=)i Fc(\033)863 2003 y Fa(2)894
1996 y Fb(\016)e Fc(\033)958 2003 y Fa(1)994 1996 y Fd(ist.)1708
2098 y(\(5\))120 2200 y(4.)24 b(Dr.)d(Alfred)e(E.)i(Neumann)f(v)o
(ersuc)o(h)o(t,)f(eine)h(einfac)o(here)f(De\014nition)h(des)h(geordne-)
182 2260 y(ten)e(P)o(aares)g(als)g(\()p Fc(a;)8 b(b)p
Fd(\))17 b(=)h Fb(f)p Fc(a;)8 b Fb(f)p Fc(b)p Fb(gg)18
b Fd(zu)h(geb)q(en.)f(Finden)h(Sie)f(ein)g(Beispiel,)e(in)j(dem)182
2320 y Fb(f)p Fc(a;)8 b Fb(f)p Fc(b)p Fb(gg)13 b Fd(=)g
Fb(f)p Fc(c;)8 b Fb(f)p Fc(d)p Fb(gg)16 b Fd(gilt,)g(ab)q(er)g(nic)o(h)
o(t)f Fc(a)f Fd(=)g Fc(c)i Fd(und)g Fc(b)e Fd(=)g Fc(d)p
Fd(.)425 b(\(5\))60 2434 y(Abgab)q(e:)16 b(F)l(reitag,)f(27.10.2000,)i
(9.00)g(Uhr,)903 2424 y(\177)897 2434 y(Ubungsk)1084
2436 y(\177)1084 2434 y(asten)f(im)e(1.)i(Sto)q(c)o(k)f(des)h(Mathema-)
60 2494 y(tisc)o(hen)f(Instituts.)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF