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

%%EndSetup
%%Page: 1 1
1 0 bop 162 274 a Fi(Mathematisc)n(hes)17 b(Institut)659
b(WS)19 b(2000/2001)162 334 y(der)f(Univ)n(ersit)487
336 y(\177)487 334 y(at)g(M)609 336 y(\177)607 334 y(unc)n(hen)828
b(Blatt)18 b(9)162 394 y(Prof.)g(Dr.)h(B.)f(P)n(areigis)307
632 y Fh(Lineare)23 b(Algebra)g(und)g(analytisc)n(he)h(Geometrie)e(I)
197 714 y Fg(33.)j(Sei)14 b Ff(V)25 b Fg(ein)14 b(V)l(ektorraum)f(und)i
Ff(U)20 b Fg(und)15 b Ff(W)21 b Fg(zw)o(ei)13 b(Un)o(terv)o(ektorr)1453
716 y(\177)1453 714 y(aume)e(v)o(on)k Ff(V)c Fg(,)j(so)284
774 y(da\031)j(sic)o(h)e(jeder)h(V)l(ektor)g Ff(v)f Fe(2)f
Ff(V)27 b Fg(auf)17 b(eindeutige)e(W)l(eise)g(als)i(Summe)925
856 y Ff(v)e Fg(=)f Ff(u)d Fg(+)g Ff(w)284 938 y Fg(mit)g
Ff(u)j Fe(2)g Ff(U)k Fg(und)13 b Ff(w)i Fe(2)f Ff(W)20
b Fg(darstellen)12 b(l)1000 940 y(\177)1000 938 y(a\031t.)h(Sei)f
Ff(B)1206 945 y Fd(U)1248 938 y Fg(eine)g(Basis)h(v)o(on)g
Ff(U)18 b Fg(und)c Ff(B)1741 945 y Fd(W)284 998 y Fg(eine)h(Basis)h(v)o
(on)f Ff(W)7 b Fg(.)16 b(Zeigen)f(Sie,)g(da\031)h Ff(B)1059
1005 y Fd(U)1099 998 y Fe(\\)11 b Ff(B)1180 1005 y Fd(W)1234
998 y Fg(=)j Fe(;)h Fg(ist)h(und)g(da\031)h Ff(B)1620
1005 y Fd(U)1660 998 y Fe([)11 b Ff(B)1741 1005 y Fd(W)284
1058 y Fg(eine)k(Basis)h(v)o(on)g Ff(V)28 b Fg(ist.)993
b(\(5\))197 1152 y(34.)25 b(Sei)18 b Ff(f)23 b Fg(:)17
b Ff(V)29 b Fe(!)17 b Ff(V)30 b Fg(ein)18 b(Endomorphism)o(us)f(eines)h
(endlic)o(hdim)o(ensionalen)e(V)l(ek-)284 1212 y(torraums.)j
Ff(U)26 b Fe(\032)20 b Ff(V)32 b Fg(sei)19 b(ein)h(Un)o(terv)o
(ektorraum)d(v)o(on)j Ff(V)12 b Fg(,)19 b(der)h(mit)e(dem)h(Bild)284
1272 y(v)o(on)d Ff(f)22 b Fg(n)o(ur)16 b(den)g(Nullv)o(ektor)e
(gemeinsam)f(hat.)k(Zeigen)e(Sie:)797 1354 y(dim)o(\(Ke)o(\()p
Ff(f)5 b Fg(\)\))14 b Fe(\025)g Fg(dim)n(\()p Ff(U)5
b Fg(\))1718 1436 y(\(6\))197 1530 y(35.)25 b(De\014niere)531
1612 y Ff(f)19 b Fg(:)14 b Fc(R)641 1591 y Fb(2)671 1612
y Fe(!)g Fc(R)774 1591 y Fb(2)791 1612 y Ff(;)8 b Fg(\()p
Ff(x;)g(y)r Fg(\))k Fe(7!)i Fg(\()p Ff(x=)p Fg(3)e(+)f(2)p
Ff(y)r(=)p Fg(3)p Ff(;)d(x=)p Fg(3)k(+)f(2)p Ff(y)r(=)p
Fg(3\))304 1694 y(\(a\))25 b(Zeigen)16 b(Sie,)f(da\031)i
Ff(f)f Fe(\016)11 b Ff(f)19 b Fg(=)14 b Ff(f)22 b Fg(ist.)302
1767 y(\(b\))i(Bestimm)o(en)d(Sie)i(Kern)g(und)h(Bild)e(v)o(on)i
Ff(f)5 b Fg(.)23 b(Zeic)o(hnen)f(Sie)h(Ke\()p Ff(f)5
b Fg(\))24 b(und)391 1827 y(Bi)o(\()p Ff(f)5 b Fg(\))23
b(in)f(ein)f(Ko)q(ordinatenkreuz)i(ein)e(und)i(b)q(esc)o(hreib)q(en)e
(Sie)h(anhand)391 1887 y(dieses)16 b(Bildes)f(die)g(Abbildung)h
Ff(f)5 b Fg(.)1718 1981 y(\(4\))197 2074 y(36.)25 b(Sei)15
b Ff(K)k Fg(ein)c(K)538 2076 y(\177)538 2074 y(orp)q(er)h(mit)d
Ff(q)k Fg(Elemen)o(ten.)12 b(Zeigen)j(Sie,)f(da\031)i(die)f(Zahl)g(der)
h(Basis-)284 2135 y(familien)d(v)o(on)k Ff(K)607 2117
y Fd(n)646 2135 y Fg(durc)o(h)585 2217 y(\()p Ff(q)628
2196 y Fd(n)662 2217 y Fe(\000)11 b Fg(1\)\()p Ff(q)798
2196 y Fd(n)832 2217 y Fe(\000)g Ff(q)r Fg(\)\()p Ff(q)968
2196 y Fd(n)1001 2217 y Fe(\000)g Ff(q)1075 2196 y Fb(2)1094
2217 y Fg(\))g Fe(\001)g Ff(:)d(:)g(:)i Fe(\001)h Fg(\()p
Ff(q)1285 2196 y Fd(n)1319 2217 y Fe(\000)g Ff(q)1393
2196 y Fd(n)p Fa(\000)p Fb(1)1461 2217 y Fg(\))284 2299
y(gegeb)q(en)16 b(ist.)1183 b(\(5\))162 2381 y(Abgab)q(e:)15
b(Mitt)o(w)o(o)q(c)o(h,)e(17.1.2001,)j(12.00)g(Uhr,)1052
2370 y(\177)1045 2381 y(Ubungsk)1232 2383 y(\177)1232
2381 y(asten)g(im)d(1.)h(Sto)q(c)o(k)h(des)f(Ma-)162
2441 y(thematisc)o(hen)g(Instituts.)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF