From 7ca0ed6b8e7d5cd847d84332f3cea988c176d618 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Beat=20J=C3=A4ckle?= Date: Wed, 30 Jun 2021 10:07:55 +0200 Subject: [PATCH] =?UTF-8?q?4.4=20=C3=9Cbungen=20-3g)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 4-4.pdf | Bin 104115 -> 104316 bytes 4-4.tex | 19 +++++++++++++++++++ 2 files changed, 19 insertions(+) diff --git a/4-4.pdf b/4-4.pdf index e991dfe9cf5f8892a3103ac18c507cab56b9f70f..7e91099330e9d1af5f562217830ef32ded0572f1 100644 GIT binary patch delta 3603 zcmV+u4(#!>tp@zA2C#h*12{1^lVL3=f9+gLZyYxgzUx=?VGko@n}{q>E8Ig7xsdo*H`tm0QsR{7<{*^_Tk7D|a= z3=|jd3uA>1SU6_{pe`=1iXS&G?%#j7e0yG^+FaAW&TQcPr;G2Nd<(t^B3Q8Te@%tL zfi6nrg#uN-`6`Y(`}@V&r!!SZ`lAX*Zv-fuL1E~{cOTDw{7Dv9^tgthCy7Ziz)JC@p0an>y0EX>so6O5Hc(BD-Ue=CE4un4m7 zg+jJ52e~CItr0SWq690PQ)8x(gFDS49jO%1LWM?iUcQk=otH++O$o2+b^m)`KRb03 zf4IE5YPOzoz=6myURoaUD#$LoI^VEl1x-DS37gvSh1nN@X!@ zLL5k>0dX91*hw0KK6F+re_aqspwZ4)FtlToWY|yxLD2(D#|7jFltM{G`^y+++LLza zP!O&I*Z0h}g3z+t)^mO_qdMZ=GgA<|z3QnqlEtue1rlYDDEM58fu!AOEUcBnlgl$9 z#x#+OuO(8Pt=3ItwD5iam6YXV{cYTr#>O~4V>qCN2EXKVp+AgleNJOx48^31uOSmvWHIN&ZB-(`vOC(7( zl0;83`F_K(p+qUPR=Ir5;_E8HuA42|W{Z077VZ2k+D1+IRnrIu;1pq**F+>(Xkf;4Qy>ZBT+2jPlzlBAuK^k`kL z3<`@;LXNqjxZ@xNc|w%byi0g^YLvu<+C!UxlJps0u^elie=rsfJ7+R(bT9@h?^Cw& zn}wxMIg{ncOt)moIL=2OH$E)GsyMg8#4S0Yd(?@~d)BJ^K!!RR^~kMy;JbE1g{G4r zuO))N3m%_9b4n=Ch5VGt_}l&J76kbcIiTQRZR;xUD?RK*a^zDvQmbm)h*3uffc>zB zRZOy3W&2off7g0)i~T9YUN=O?$i_rJ%y2?XUbVGHC~Kc7YdB6@TNIMEv5vO>@=)d; z3}t>6%38|S@(AK=fjL&7*_@saGLz>TwAUHPj!@+4Bw=pOI^i96L}_s9=@?BK3#+gj z3~Ms5o_rT$ErqClDi|gnk~cmc3~LjFqafH&Tn$>aeF zCL-c=IuoHa3UZ%H6O%FZxT`+PxBbuOkC(SMcQ@CcueV%AkK!{@52=5b>T-jP8hY7& zNr9Yme}nHVIX`w!3WL0R(rU`>>gzTZi+UTowHXzd1#AO887s6g%S=YCbF~0D@V|B= z#CmsUrfx=R@9HC9|&W# z4^oWCHfvLHMXpp}5=t`ne|B`(fALH7Rc-8mun=W7D8vE9vX^~3%4 zs{b~-^&RY=tg#`pcf7`aIJiDIdLCRp{?KqG7lPa}GC1{RhVFInk|2>hrKm84z$sZNo!`(r)JIfD-+-u^JgX8GZ47xmnF1t7XkSN0vavfLM z=9%D#1q8lUe()zcjz`CeyIZKZ)`eDA%`=jaj^X4mBh6l;f;9(Fp3Rb_b{;4V!iI(z ztnj2uONx$Md%J$!CA0yBC7DbU+U21ae}v`yoOJ;dx9{Z2M?Cg(wIRPK{=?oada`Ti z$Y_NV#jc4maQwwkpHECvk8)Z@VLb=s=;ULQD~+|b4*xH=t=IIW3NJfQay?mE!a13Eq0KJ5-ZUJcD}fx8qQa`f56Wg zgzU@ko^#VFfqm+;p6@khJ}fyC-AtFax3QSc!{+Ly`S9WP`lgB4w)HnJ?(gm{KeRvH z-E6P^T7P`|Iclk>uI}T9{H@<^KGz?%@$38Mhh8_*50&DJ^Hg76|9pA-Yx{N;8O9I) zJ|}nS4O&a9Y`1Zl>-Z`D5;s?ue|NP&1W)J~Bt+nMU4H+MA8Ort8>hIt-U{wy$@#7> zK%-9eJp;qo0rz*VPtQxQ9I^-OgXphb7Zny~(za8j*$doh3N?Y`F)P&EXNM2fBVG&W zBq|Uesqt}@$0?WUhkAUHpW-Kh_BCL>8)#?mL@IHws)}E z=D=57Zwq&~Uk8s|hvs$8T+oYw9Og`tbQkcJ+SF>iB=0{Uv}YF`#6Bt}@$!b`NVZ<` zXt_)l6e9)nCXZ^NO=c}lXK2&h42y<=9M zA$$l`_3p947t5aYe<4Q&Ll>wf*rs-S1qbnrCPHQ+9 zzK7mp`U~H@5599I>dxG%h*J$kJz0L&FYAwT?jplVNKyx}H{$5T@+Vq`+4!9x~S`xjnOm(=?w#E~hV&?RYpe>uJ)S5e#wS2;3;qaCZO zR}q-qrl91W_mMkYAxlqjS;@4^^BFr!QbMcu#WrIzxc=ht*csGBzp9NycSA^!*8Y~n=}Fq zMuAct)92q!1+Ge7X1z0h(C2Tfx_HC=CpfGR`cRFfkB&Qea@_gZxU&Z-mQrg=%ed+q zI$1GV6vsMD^}}?S6;7Ars5r(D`OXTZ2LHpx{{UXR z@b`n-8@JjU0pMr`F)%PUF*KLJgaI7}F)%PUF*LX1gaOJ9Q8Pm}H$*uzFhesoIYl`_ zLOC--G(|ErHbXTvHZnmnL_Q!qGeb5vL^(4sLo+rxML9x3IWt2vMKUxtLp3!vGC?v# zK3xhgOl59obZ8(pFgcSUD=B{+(pyjsP!tB>y>cn(q9}55R7aie_Y_i;5E{9SVvdw4 zL{y4!a4IL)$|R)RRYE0|2Qy~yPK-ehZsUQ$@Y0MPyyXA)%QtJ*-m});Yj35L8go#} zMTiom+!Z5#GK=_-a1u$PNd)l_sY}u%1;mdB8$8?gChKk6Aj?x8*rL`%amH{6MG&L~_B_%~qMhaAA%%A`O delta 3429 zcmV-r4Vv=&t_HKM2C#h*12!=-lhGV0e_KnB95oQW@2}_shgm^8cKMws5(zH_aY3wd zAsi-|Nm$qnB+ClKuczEkyQkdKJ=3!Z2qDrlvu?Yp{MFOtr&kvbzLvZYf_bf>xO!b^ z!;F`OwVHuc#nq5e@pZ zVKQDae3D4njJ1GR%QEYHyw+osf2))$O~|#>xE0FboV7F>!It30#H$3;RxBc3rJ2y~ zRF=;rUO7X&iWIL$yh0;hlZv+lJ0@iC%!p+$EF}XDlNeWd#(N>FWrW;Jqeg|S5+O@c z$c{Os2N-^ym#nbNm}TG#0@cT!%I&!%t7k|Srdo#)!E(*;|3w7LJp(@rf3onALbh=S zsV6LrX59Ot1jDQqIaf%*9cSSdO$sO`d}BG+FSr($rRIE9!n1nazwhd2XKuom^=8wM z9!tOiQ-OBHcnjti9BAJn(Q%g+Ws^u9bWEXQUa3~1FF5D4xDZ*qH8-U&(yx3Nh^zrh z98%bE93q|XyjZ-TM1_`Sf5L*k9V0j)h8hS0AD}xaNQyzu1Q$qOA~4enQ>E~4zJA<;A>s)Hn&=_H!QOt?kOM9Oh(Aoy&#CE%%*RtnS)5#^vb*isn%%2ukSse~A5%$uG*FMmF7anS1e&$3XWboIyQjp39lgcMK!2gUFu>D<302 z?0o<1eTf|Uk|h?@%|bTzOoIi@MCWDaEF2cZVJp%m)!;k|S7?(sQc~ih4ZRX5%ti?Y z<^uDMqYUI3QBun;lHs{g5*BJVZ30T-XL!X>qP0vLIBuWOf4SktXjw&{yw%?%EqzG2 zEQ@ZsWs8S#F2uOuVF*!$xrL0vk~4-!o%*~cy}I-0sDo1v(y9l(Y6&V7?gU0H0sLL^ z_yC$+l1y5k?ot{4df40o!&o8(6dY}BZ54gRn>|a9T&zc8QEMA8Y7qf&7}l_eOV*2! zFKcp*!?4($e?#q6!*s}Obcn+=rNkIj8*_rOc8Rfu)2y|Tj3XJ#SnH1uW%k}s<|d)6 z+G zcG1RQit5IaVU!_8(j{bbmpe^Z8Ili^VgC6Vqchir&tICSXk z{6r2V#i2^eZ6IUnGh7-5&}j*^g+3HL4!x@q9*V<(A;jH@7|c{60#3&( z5lTsh;ZvzYF{U23>8pIZ-`>An-(25bZ{KfsR7DT-Gc*rzd>7ktEgLiRwEYniIco>M z84P~Re}NJPM)zpdgx$B-Z7vqOkk3*4dkQ^Q(Dh+8MVz-4EP}a+RqSc>Nr_| zsCH;}iA1KkSsD?0G{J5*Gbejdmn}aa#$1b3LE+;I0v}(*_^=}pN^mYZ4hqW2p-EBl z{SxqAwc>ers$4juP=E44^K=!khr*sp16-P4fAT2LtmD9p2J9uHLwm1qi{JVkhMZnw53rPO0@E%eJ33Y}Z3~AIv6$kU^QUtmjfi82f{ty|%5>gvi`R0k>2n__T zHh%CwI!;H&g4E44T+2eM>*mQ6q(eG6tVol`s9^LFoF}s+rJZ{!gOI7A^oBXKr6p!Z zwmn_nb_H#a%%D!j1?}?K1Hy88&AI^0f7|zJ<(Y{6Qmim83jdI2iw^yowCJ?_nR3_2 z7+CsXsIMo+rAI!lqp)0na&qypsg;IaTPy#QWUD2kvy+<|Xj2Ib#CRj7GIUZ@6_OG> zj%*C=mut#e;#6J_x!$LjcgKO&b(xA!d$B!_j94kPC+7<*is5{v_4KTs@xBf3e=#+k zV6rcL*7H55+=sznqMK=ba}%2B9IQ6i&4)KP+v_G{+tt53xx2kxziGeSUhg)a)gNEJ z4^}FetGn=5^W$A>K`lHubjm3$!?R9DP3U{7HO+bB28Z{63;bZNHQw%zd`h{Q#!v%Ak z1ov376ibk0=^c5?f+I&JK4TG40UMG|ISXiTbkzhIY~}KsQiXG*UC}tqe+?KJ%*I7G z;8UClfNXHaHJJw=GYmO~r59COWWw+>a&h0AsfSe4BWJwF%`}t%;q~ ziBuu$J#+ix_x305C?UNvgku`Bus*>u`tR=}ya(pBGU9G3czf#L5$tPeRqbd#dt< zwr6$BRzbc$|E$V~e;VO1?+gcjp-|j6?(wp6z+=ZW{nhUf3UR-8HJnP{eIGG>LSNno z*98;x&D^SqQw&u-T7Ew+>$h_1BEwEdGzZ~s#L0!_qmJ0mh|t*=k^(|qca~I|y4Nv# z-j%ar=t8-c$1E%kFT9{Fsp&_=p(`J;C2@T@yuueT+(It0MP))}Z>%ofMWFXD1x4q) zANZy#B;_fpDjDDMd_>L?wa}_VxlL{c+aElhI)fOwuWClSM76FPv_-gREA-%Q??1SA zOx}|b9utGQ9Jjh00nKOzFgZ0eH8Youg#jG~FgZ0eH8Z!cg#pSAQA9X2F*!ywHaRyj zH8eOwI7T@*K|w_{GC4yvMK?h~L_Q!qL^w1tIYu-#IX5viG&n;zMmab^K}9q&IYTu? zH$g!}K3xhgOl59obZ8(pF*B0^O(}mJ(pyjrP#6dB^KD{F+BTtV+jd*sFDiy;v?*$2 zlS?jzj5I6JRLYV|bQu&<8j%#0ViJiN4<0b%$?#+b<>Ydfan|$lMP}EK%6&-_Xi1iATbLh zb%W#qkYd-}yofiMNqj`5vRhgWSkw#_zXwZFz|ty^-UybBg5{GS;~rSy1v1ltBNt>j z!OC)w?E*O+x{)t25kFC@CiQ=sKbcJe$Q&}4%p-xKR`;Ml?hlYR1=je2d@ERM1kO@W zkfTe@Cl(ScYMluig_U5v9c*BgO+lcj5NvJ*TONb0JbiH>DB;vf*kk)|u;UBZ`2m!2 zZP#nCI|h^;1$%};`5)lQ2YYKl#W#J75Mm>tqAD}7vA-Q0cm%4xgKB>Rs8OJnmpNzw zbv$m}XHee>4zY)u6L)_Chu?xDeDemT9J7Jr4sc>4Xxs))@>-|(s!he9xgWH!O6xOl z+7q1N-#D8A+V+9=C*a&5IL~Li@E2TkgU$)i#rt0R3cC6KE_;9;Gx-IsCV*a!vzKGK z_7e1c1lRjOKbsFUfg67v;3j7^_!JCrcbMgGT>&FZ8Epf%Uw}J&z1|C%F5r>lq5-DnONUzyNy%8NP5cSVnM^Pf-P8~&yINs?fMx?Y`N3kLeuXGeg z(nOjolt`CT{Rhnsk3|Y)Ze(+Ga%Ev{3T19&Z(?c+b97;Hba)YRWo8O7Ff%eVHVP#r HMNdWwf@w+1 diff --git a/4-4.tex b/4-4.tex index 98a5bea..47db7d1 100644 --- a/4-4.tex +++ b/4-4.tex @@ -292,6 +292,25 @@ $\left(\begin{matrix} \end{matrix}\right)$ $\Rightarrow\mathbb{L}=\{(1,4,0,1)\}$ +\item (-3)I zu III add +$\left(\begin{matrix} +1&-1&4&1\\ +0&0&2&3\\ +0&0&-7&-3 +\end{matrix}\right)$ +II zu III add +$\left(\begin{matrix} +1&-1&4&1\\ +0&0&2&3\\ +0&0&-5&0 +\end{matrix}\right)$ +$\frac{2}{5}$III zu II add +$\left(\begin{matrix} +1&-1&4&1\\ +0&0&0&3\\ +0&0&-5&0 +\end{matrix}\right)$ +II ist nun $0=3\Rightarrow\mathbb{L}=\{\}$ \end{enumerate} \end{document} \ No newline at end of file