%!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: WS0001Ub8V3.dvi %%Pages: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips WS0001Ub8V3.dvi %DVIPSParameters: dpi=300, compressed, comments removed %DVIPSSource: TeX output 2001.01.04:1529 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 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y(es)d(einen)g(v)o(on)g(Null)g(v)o(ersc)o (hiedenen)e(V)l(ektor)i(\()p Fe(a;)c(b)p Ff(\))13 b Fd(2)h Fe(K)1324 1380 y Fc(2)1356 1398 y Ff(und)f(eine)e(Zahl)i Fe(c)h Fd(2)g Fe(K)284 1458 y Ff(gibt,)i(so)h(da\031)692 1518 y Fe(G)d Ff(=)g Fd(f)p Ff(\()p Fe(x;)8 b(y)r Ff(\))13 b Fd(2)h Fe(K)1040 1498 y Fc(2)1074 1518 y Fd(j)f Fe(ax)e Ff(+)g Fe(by)k Ff(=)f Fe(c)p Fd(g)284 1599 y Ff(Zw)o(ei)h(Geraden)i Fe(G)633 1606 y Fc(1)670 1599 y Ff(und)g Fe(G)806 1606 y Fc(2)826 1599 y Ff(,)f(die)g(durc)o(h)g(die)g(V)l(ektoren)g(\()p Fe(a)1404 1606 y Fc(1)1423 1599 y Fe(;)8 b(b)1466 1606 y Fc(1)1486 1599 y Ff(\))16 b(bzw.)g(\()p Fe(a)1680 1606 y Fc(2)1700 1599 y Fe(;)8 b(b)1743 1606 y Fc(2)1762 1599 y Ff(\))284 1659 y(gegeb)q(en)21 b(sind,)f(hei\031en)g(parallel,)f(w)o (enn)i(die)f(V)l(ektoren)f(\()p Fe(a)1412 1666 y Fc(1)1431 1659 y Fe(;)8 b(b)1474 1666 y Fc(1)1494 1659 y Ff(\))20 b(und)h(\()p Fe(a)1680 1666 y Fc(2)1700 1659 y Fe(;)8 b(b)1743 1666 y Fc(2)1762 1659 y Ff(\))284 1719 y(linear)14 b(abh)496 1721 y(\177)496 1719 y(angig)j(sind.)d(Zeigen)h(Sie:)f(Zw)o (ei)g(nic)o(h)o(t)f(parallele)h(Geraden)h(b)q(esitzen)284 1780 y(genau)f(einen)f(Sc)o(hnittpunkt.)f(\(Hin)o(w)o(eis:)f(Zeigen)i (Sie)g(zun)1367 1782 y(\177)1367 1780 y(ac)o(hst:)g(Die)g(V)l(ektoren) 284 1840 y(\()p Fe(a)329 1847 y Fc(1)348 1840 y Fe(;)8 b(b)391 1847 y Fc(1)410 1840 y Ff(\))16 b(und)h(\()p Fe(a)588 1847 y Fc(2)607 1840 y Fe(;)8 b(b)650 1847 y Fc(2)669 1840 y Ff(\))16 b(sind)g(genau)h(dann)f(linear)g(unabh)1337 1842 y(\177)1337 1840 y(angig,)h(w)o(enn)e(die)h(V)l(ek-)284 1900 y(toren)i(\()p Fe(a)458 1907 y Fc(1)477 1900 y Fe(;)8 b(a)525 1907 y Fc(2)544 1900 y Ff(\))19 b(und)f(\()p Fe(b)721 1907 y Fc(1)740 1900 y Fe(;)8 b(b)783 1907 y Fc(2)803 1900 y Ff(\))18 b(linear)f(unabh)1109 1902 y(\177)1109 1900 y(angig)j(sind.)d(Sie)h(sind)g(dann)g(sogar)284 1960 y(erzeugend.\))1189 b(\(7\))197 2058 y(31.)25 b(Bestimm)o(en)13 b(Sie)i(jew)o(eils)g(eine)g(Basis)h(der)g(folgenden)g(Un)o(terv)o (ektorr)1577 2060 y(\177)1577 2058 y(aume)d(v)o(on)284 2118 y Fa(R)323 2100 y Fc(3)356 2118 y Ff(bzw.)j Fa(R)509 2100 y Fc(4)525 2118 y Ff(:)372 2213 y Fe(U)405 2220 y Fc(1)439 2213 y Ff(:=)d(Span)q(\()p Fd(f)p Ff(\(1)p Fe(;)8 b Ff(1)p Fe(;)g Fd(\000)p Ff(1\))p Fe(;)g Ff(\()p Fd(\000)p Ff(1)p Fe(;)g Fd(\000)p Ff(1)p Fe(;)g Fd(\000)p Ff(1\))p Fe(;)g Ff(\()p Fd(\000)p Ff(1)p Fe(;)g Fd(\000)p Ff(1)p Fe(;)g Fd(\000)p Ff(3\))p Fe(;)g Ff(\(1)p Fe(;)g Ff(1)p Fe(;)g Fd(\000)p Ff(3\))p Fd(g)p Ff(\))372 2286 y Fe(U)405 2293 y Fc(2)439 2286 y Ff(:=)13 b Fd(f)p Ff(\()p Fe(x)576 2293 y Fc(1)596 2286 y Fe(;)8 b(x)646 2293 y Fc(2)665 2286 y Fe(;)g(x)715 2293 y Fc(3)734 2286 y Fe(;)g(x)784 2293 y Fc(4)803 2286 y Ff(\))14 b Fd(2)g Fa(R)922 2265 y Fc(4)953 2286 y Fd(j)f Fe(x)1008 2293 y Fc(1)1042 2286 y Ff(=)h Fe(x)1122 2293 y Fc(2)1141 2286 y Fe(;)8 b(x)1191 2293 y Fc(3)1224 2286 y Ff(=)14 b Fd(\000)p Fe(x)1343 2293 y Fc(4)1362 2286 y Fd(g)284 2381 y Ff(Bestimm)o(en)f(Sie)i(jew)o (eils)g(Elemen)o(te)e(der)j(k)m(anonisc)o(hen)g(Basis,)g(die)f (zusammen)284 2441 y(mit)21 b(den)i(angegeb)q(enen)h(Basen)f(v)o(on)g Fe(U)1054 2448 y Fc(1)1097 2441 y Ff(und)g Fe(U)1234 2448 y Fc(2)1277 2441 y Ff(Basen)g(v)o(on)g Fa(R)1565 2423 y Fc(3)1605 2441 y Ff(bzw.)f Fa(R)1764 2423 y Fc(4)284 2501 y Ff(ergeb)q(en.)1256 b(\(4\))p eop %%Page: 2 2 2 1 bop 197 274 a Ff(32.)25 b(Betrac)o(h)o(ten)14 b(Sie)i(folgende)g(V) l(ektoren)f(im)g(V)l(ektorraum)f Fa(Q)1387 256 y Fc(2)1408 274 y Ff(:)572 384 y Fe(w)607 391 y Fc(1)641 384 y Ff(=)f(\(1)p Fe(;)8 b Ff(2\))99 b Fe(w)934 391 y Fc(2)967 384 y Ff(=)14 b(\(2)p Fe(;)8 b Ff(1\))98 b Fe(w)1260 391 y Fc(3)1293 384 y Ff(=)14 b(\(1)p Fe(;)8 b Fd(\000)p Ff(1\))284 494 y(En)o(tsc)o(heiden)15 b(Sie)h(in)g(den)h(folgenden)f(drei)g(F)1133 496 y(\177)1133 494 y(allen,)f(ob)i(es)g(eine)e(lineare)h(Abbil-)284 554 y(dung)k Fe(f)25 b Ff(:)19 b Fa(Q)529 536 y Fc(3)569 554 y Fd(!)h Fa(Q)677 536 y Fc(2)717 554 y Ff(mit)e(der)h(Eigensc)o (haft)h Fe(f)5 b Ff(\()p Fe(v)1234 561 y Fc(1)1253 554 y Ff(\))20 b(=)g Fe(w)1385 561 y Fc(1)1404 554 y Ff(,)f Fe(f)5 b Ff(\()p Fe(v)1509 561 y Fc(2)1529 554 y Ff(\))20 b(=)f Fe(w)1660 561 y Fc(2)1700 554 y Ff(und)284 614 y Fe(f)5 b Ff(\()p Fe(v)356 621 y Fc(3)375 614 y Ff(\))14 b(=)g Fe(w)495 621 y Fc(3)531 614 y Ff(gibt:)304 716 y(\(a\))25 b Fe(v)415 723 y Fc(1)448 716 y Ff(=)14 b(\(1)p Fe(;)8 b Ff(0)p Fe(;)g Ff(0\))p Fe(;)g(v)700 723 y Fc(2)734 716 y Ff(=)14 b(\(0)p Fe(;)8 b Ff(1)p Fe(;)g Ff(0\))p Fe(;)g(v)986 723 y Fc(3)1019 716 y Ff(=)14 b(\(0)p Fe(;)8 b Ff(0)p Fe(;)g Ff(1\))302 797 y(\(b\))24 b Fe(v)415 804 y Fc(1)448 797 y Ff(=)14 b(\(1)p Fe(;)8 b Ff(0)p Fe(;)g Ff(0\))p Fe(;)g(v)700 804 y Fc(2)734 797 y Ff(=)14 b(\(0)p Fe(;)8 b Ff(1)p Fe(;)g Ff(0\))p Fe(;)g(v)986 804 y Fc(3)1019 797 y Ff(=)14 b(\()p Fd(\000)p Ff(1)p Fe(;)8 b Ff(1)p Fe(;)g Ff(0\))307 878 y(\(c\))24 b Fe(v)415 885 y Fc(1)448 878 y Ff(=)14 b(\(1)p Fe(;)8 b Ff(0)p Fe(;)g Ff(0\))p Fe(;)g(v)700 885 y Fc(2)734 878 y Ff(=)14 b(\(0)p Fe(;)8 b Ff(1)p Fe(;)g Ff(0\))p Fe(;)g(v)986 885 y Fc(3)1019 878 y Ff(=)14 b(\(1)p Fe(;)8 b Ff(1)p Fe(;)g Ff(0\))284 980 y(En)o(tsc)o(heiden)16 b(Sie)g(in)h(jedem)f (dieser)g(F)1009 982 y(\177)1009 980 y(alle)g(auc)o(h,)h(ob)h(eine)e (solc)o(he)h(lineare)f(Ab-)284 1040 y(bildung)g(durc)o(h)g(diese)f (Bedingung)h(eindeutig)g(b)q(estimm)o(t)d(ist.)264 b(\(3\))162 1154 y(Abgab)q(e:)15 b(Mitt)o(w)o(o)q(c)o(h,)e(10.1.2001,)j(12.00)g (Uhr,)1052 1143 y(\177)1045 1154 y(Ubungsk)1232 1156 y(\177)1232 1154 y(asten)g(im)d(1.)h(Sto)q(c)o(k)h(des)f(Ma-)162 1214 y(thematisc)o(hen)g(Instituts.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF