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z?P{Z+jlb2pO$NiZW8r_*)hCTTo9%A5WfRpt97dsa8dO=s&HABTN#$hqe;tr7OxrDD zcasX#h)dx8l)qpLq?&jgD1e$#J4wtl_!2<2){T_`&&U}t+cX74v$g^Z_lD3DpTYyD z6Z|hJnZ}JzSY1&Tw20`AZnSu}00NhoKq6ukcQfzyKknuRSpdx~Bap=`3=R9$Wu0T1 zY)$w^$FXy`4is*;vhN3x&TXZF^yD6esklx1YI&=lSe)(@LZ*B_-M^>oOSvmoa62RE*DMGF&bkl^~; zI_pe$bHTnn1f%|TKTVzDL%LNCynS#c(x{jsH@4~!`T-HHbC^%T@Rd)h3a-yM9ci6CZA&!7f)4-kUtiutHR zE;pw6IU~3cpe|*KH!f~Uq%Jxpj<1&ckqn0JrvqE_t<2fc*}n1J3QFh-ME)BpM(>rP zTmKQ{-Zc-SinT934lR}uv9C1NhHZ~PKRowppfr68Z diff --git a/docs/loesungen.tex b/docs/loesungen.tex index f46c748..09dfa74 100644 --- a/docs/loesungen.tex +++ b/docs/loesungen.tex @@ -6832,14 +6832,14 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve \begin{mathe}[mc]{rcccccl} \phi(x) - &= &\begin{vector} 2x_{2}\\ 3x_{1}-4x_{3}\\\end{vector} + &= &\begin{vector} 2x_{2}\\ 3x_{1}-x_{3}\\\end{vector} &= &\begin{vector} 0\\ 3\\\end{vector}x_{1} + \begin{vector} 2\\ 0\\\end{vector}x_{2} - + \begin{vector} 0\\ -4\\\end{vector}x_{3} + + \begin{vector} 0\\ -1\\\end{vector}x_{3} &= &\underbrace{ \begin{matrix}{rrr} 0 &2 &0\\ - 3 &0 &-4\\ + 3 &0 &-1\\ \end{matrix} }_{=:C} x.\\ @@ -6856,7 +6856,7 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve \begin{mathe}[mc]{rcccl} CB &= &\begin{matrix}{rrr} 0 &2 &0\\ - 3 &0 &-4\\ + 3 &0 &-1\\ \end{matrix} \begin{matrix}{rrr} 1 &1 &0\\ 1 &-1 &3\\ @@ -6865,7 +6865,7 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve &= & \begin{matrix}{rrr} 2 &-2 &6\\ - 3 &-5 &4\\ + 3 &1 &1\\ \end{matrix} .\\ \end{mathe} @@ -6875,7 +6875,7 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve \begin{mathe}[mc]{rcl} \begin{matrix}{rr|rrr} 2 &-1 &2 &-2 &6\\ - 1 &1 &3 &-5 &4\\ + 1 &1 &3 &1 &1\\ \end{matrix} &\xrightarrow{ Z_{2}\mapsfrom 2\cdot Z_{2} - Z_{1} @@ -6883,7 +6883,7 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve & \begin{matrix}{rr|rrr} 2 &-1 &2 &-2 &6\\ - 0 &3 &4 &-8 &2\\ + 0 &3 &4 &4 &-4\\ \end{matrix} \\ &\xrightarrow{ @@ -6891,8 +6891,8 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve } & \begin{matrix}{rr|rrr} - 6 &0 &10 &-14 &20\\ - 0 &3 &4 &-8 &2\\ + 6 &0 &10 &-2 &14\\ + 0 &3 &4 &4 &-4\\ \end{matrix} \\ &\xrightarrow{ @@ -6903,15 +6903,15 @@ Das Hauptziel hier ist, eine Variant anzubieten, gegen die man seine Versuche ve } & \begin{matrix}{rr|rrr} - 1 &0 &5/3 &-7/3 &10/3\\ - 0 &1 &4/3 &-8/3 &2/3\\ + 1 &0 &5/3 &-1/3 &7/3\\ + 0 &1 &4/3 &4/3 &-4/3\\ \end{matrix} .\\ \end{mathe} Darum gilt $M^{\cal{B}}_{\cal{A}}(\phi)=A^{-1}CB=\boxed{\begin{matrix}{rrr} - 5/3 &-7/3 &10/3\\ - 4/3 &-8/3 &2/3\\ + 5/3 &-1/3 &7/3\\ + 4/3 &4/3 &-4/3\\ \end{matrix}}$. Zur Untersuchung der Injektivität/Surjektivität von $\phi$,