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"" 0 1 0 0 0 0 1 2 0 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 0 1 0 0 0 1 0 0 0 2 2 2 0 0 0 1 }{PSTYLE "_pstyle1" -1 200 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_ps tyle2" -1 201 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 1 0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_cstyle1" -1 203 "C ourier" 1 10 0 0 255 1 0 0 0 2 2 2 0 0 0 1 }{PSTYLE "_pstyle3" -1 202 1 {CSTYLE "" -1 -1 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }3 3 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle4" -1 203 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 21 "restart:with(linal g):" }}{PARA 201 "" 1 "" {TEXT 203 79 "Warning, the protected names no rm and trace have been redefined and unprotected" }{TEXT 203 1 "\n" }} }{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 38 "#zh/3 Berechnung von A.v \+ und InversA.w" }{MPLTEXT 1 0 37 "\nA:=matrix(3,3,[1,0,2,0,1,0,3,-1,0]) ;" }{MPLTEXT 1 0 16 "\nAI:=inverse(A);" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"AG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7%7%\"\"\"\"\"! \"\"#7%F/F.F/7%\"\"$!\"\"F/" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I#AIG 6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7%7%\"\"!#\"\"\"\"\"$F/7%F. F0F.7%#F0\"\"##!\"\"\"\"'F6" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 25 "v:=[2,3,-4]; w:=[-1,3,6];" }{MPLTEXT 1 0 31 "\nevalm(A &* v); ev alm(AI &* w);" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"vG6\"7%\"\"#\"\" $!\"%" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"wG6\"7%!\"\"\"\"$\"\"'" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslib G6\"6#7%!\"'\"\"$F," }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I* protectedGF&I(_syslibG6\"6#7%\"\"$F+!\"#" }}}{EXCHG {PARA 200 "> " 0 " " {MPLTEXT 1 0 45 "#zh/1 Diskussion des Gleichungssystems nach a" } {MPLTEXT 1 0 54 "\nM:=matrix([[0,1,1,1],[1,0,1,1],[1,1,0,1],[1,1,a,0]] );" }{MPLTEXT 1 0 22 "\nb:=vector([1,2,3,0]);" }{MPLTEXT 1 0 21 "\nlin solve(M,b,'r',v);" }{MPLTEXT 1 0 63 "\nMb:=matrix([[0,1,1,1,1],[1,0,1, 1,2],[1,1,0,1,3],[1,1,a,0,0]]);" }{MPLTEXT 1 0 19 "\nrank(M); rank(Mb) ;" }{MPLTEXT 1 0 14 "\ngausselim(M);" }{MPLTEXT 1 0 16 "\n#M quadratis ch!" }{MPLTEXT 1 0 15 "\ngausselim(Mb);" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"MG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&\"\"!\"\"\" F/F/7&F/F.F/F/7&F/F/F.F/7&F/F/I\"aGF%F." }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"bG6\"-I'vectorG6$I*protectedGF)I(_syslibGF%6#7&\"\"\"\"\"#\" \"$\"\"!" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF &I(_syslibG6\"6#7&*&,&\"\"\"F-I\"aGF(\"\"#F-,&F/F-F.F-!\"\"*&,&F1F-F.F -F-F0F1,$*$F0F1!\"$,$F5\"\"'" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I#Mb G6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7'\"\"!\"\"\"F/F/F/7'F/F .F/F/\"\"#7'F/F/F.F/\"\"$7'F/F/I\"aGF%F.F." }}{PARA 202 "" 1 "" {XPPMATH -1 "6#\"\"%" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#\"\"%" }} {PARA 202 "" 1 "" {XPPMATH -1 "6#-I'matrixG6$I*protectedGF&I(_syslibG6 \"6#7&7&\"\"\"\"\"!F,F,7&F-F,F,F,7&F-F-!\"#!\"\"7&F-F-F-,&F1F,I\"aGF(# F1\"\"#" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'matrixG6$I*protectedGF& I(_syslibG6\"6#7&7'\"\"\"\"\"!F,F,\"\"#7'F-F,F,F,F,7'F-F-!\"#!\"\"F-7' F-F-F-,&F2F,I\"aGF(#F2F.!\"$" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 5 "#zh/2" }{MPLTEXT 1 0 27 "\nG:=matrix([[3,3],[3,11]]);" } {MPLTEXT 1 0 17 "\neigenvectors(G);" }}{PARA 202 "" 1 "" {XPPMATH -1 " 6#>I\"GG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7$7$\"\"$F.7$F.\"#6 " }}{PARA 202 "" 1 "" {XPPMATH -1 "6$7%\"\"#\"\"\"<#-I'vectorG6$I*prot ectedGF*I(_syslibG6\"6#7$!\"$F%7%\"#7F%<#-F(6#7$F%\"\"$" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 6 "#hf3/5" }{MPLTEXT 1 0 63 "\nA5:=tr anspose(matrix(4,4,[1,0,1,0,0,1,0,1,1,2,1,3,1,-2,c,3]));" }{MPLTEXT 1 0 18 "\nA5I:=inverse(A5);" }{MPLTEXT 1 0 14 "\nv:=[1,0,0,0];" } {MPLTEXT 1 0 17 "\nevalm(A5I &* v);" }}{PARA 202 "" 1 "" {XPPMATH -1 " 6#>I#A5G6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&\"\"\"\"\"!F.F. 7&F/F.\"\"#!\"#7&F.F/F.I\"cGF%7&F/F.\"\"$F6" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I$A5IG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7&7&* &,&!\"&\"\"\"I\"cGF%F1F1,&F2F1!\"\"F1F4F1,$*$F3F4\"\"%F47&,$F6!#7\"\"$ ,$F6\"#7!\"#7&,$F6\"\"&F4,$F6F0F17&,$F6F4\"\"!F6FE" }}{PARA 202 "" 1 " " {XPPMATH -1 "6#>I\"vG6\"7&\"\"\"\"\"!F(F(" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslibG6\"6#7&*&,&!\"&\"\" \"I\"cGF(F.F.,&F/F.!\"\"F.F1,$*$F0F1!#7,$F3\"\"&,$F3F1" }}}{EXCHG {PARA 202 "" 1 "" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 48 "#hf3/9 Spiegeln an x-z=0, Rotieren um z mit pi/3" }{MPLTEXT 1 0 36 "\nS:=mat rix(3,3,[0,0,1,0,1,0,1,0,0]);" }{MPLTEXT 1 0 57 "\nR:=matrix(3,3,[1/2, -sqrt(3)/2,0,sqrt(3)/2,1/2,0,0,0,1]);" }{MPLTEXT 1 0 22 "\nv:=vector(3 ,[1,2,3]);" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 20 "lam:=eigenvalues(S) ;" }{MPLTEXT 1 0 23 "\nvecs:=eigenvectors(S);" }{MPLTEXT 1 0 20 "\nmu: =eigenvalues(R);" }{MPLTEXT 1 0 23 "\nvecr:=eigenvectors(R);" } {MPLTEXT 1 0 1 "\n" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"SG6\"-I'mat rixG6$I*protectedGF)I(_syslibGF%6#7%7%\"\"!F.\"\"\"7%F.F/F.7%F/F.F." } }{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"RG6\"-I'matrixG6$I*protectedGF)I (_syslibGF%6#7%7%#\"\"\"\"\"#,$*$\"\"$F.#!\"\"F0\"\"!7%,$F2F.F.F67%F6F 6F/" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"vG6\"-I'vectorG6$I*protect edGF)I(_syslibGF%6#7%\"\"\"\"\"#\"\"$" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I$lamG6\"6%!\"\"\"\"\"F(" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I %vecsG6\"6$7%\"\"\"\"\"#<$-I'vectorG6$I*protectedGF.I(_syslibGF%6#7%F( \"\"!F(-F,6#7%F2F(F27%!\"\"F(<#-F,6#7%F7F2F(" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I#muG6\"6%\"\"\",&#F'\"\"#F'*&^#F)F'\"\"$F)F',&F)F'*&^ ##!\"\"F*F'F-F)F'" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I%vecrG6\"6%7%, &#\"\"\"\"\"#F**&^#F)F*\"\"$F)F*F*<#-I'vectorG6$I*protectedGF3I(_sysli bGF%6#7%F*,&*&F.F)F(F*#!\"#F.*$F.F)#F*F.\"\"!7%,&F)F**&^##!\"\"F+F*F.F )F*F*<#-F16#7%F*,&*&F.F)F?F*F9F;F " 0 "" {MPLTEXT 1 0 15 "evalm(S&*R&*v);" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 15 "evalm(R&*S&*v);" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslibG6\"6#7%\"\"$,&*$F+#\"\"\"\" \"#F.F/F/,&F.F/F-!\"\"" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6 $I*protectedGF&I(_syslibG6\"6#7%,&#\"\"$\"\"#\"\"\"*$F-#F/F.!\"\",&F/F /F0F,F/" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 46 "#hf3/8 Strecke n in x um2, Rotieren um z mit 90" }{MPLTEXT 1 0 37 "\nSt:=matrix(3,3,[ 2,0,0,0,1,0,0,0,1]);" }{MPLTEXT 1 0 38 "\nRy:=matrix(3,3,[0,-1,0,1,0,0 ,0,0,1]);" }{MPLTEXT 1 0 19 "\nw:=array([3,2,1]);" }}{PARA 200 "> " 0 "" {MPLTEXT 1 0 17 "evalm(St&*Ry&*w);" }{MPLTEXT 1 0 18 "\nevalm(Ry&*S t&*w);" }{MPLTEXT 1 0 17 "\neigenvalues(St);" }{MPLTEXT 1 0 18 "\neige nvectors(St);" }{MPLTEXT 1 0 17 "\neigenvalues(Ry);" }{MPLTEXT 1 0 18 "\neigenvectors(Ry);" }{MPLTEXT 1 0 1 "\n" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I#StG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7%7%\" \"#\"\"!F/7%F/\"\"\"F/7%F/F/F1" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I# RyG6\"-I'matrixG6$I*protectedGF)I(_syslibGF%6#7%7%\"\"!!\"\"F.7%\"\"\" F.F.7%F.F.F1" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"wG6\"-I'vectorG6$ I*protectedGF)I(_syslibGF%6#7%\"\"$\"\"#\"\"\"" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslibG6\"6#7%!\"%\"\"$\" \"\"" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_ syslibG6\"6#7%!\"#\"\"'\"\"\"" }}{PARA 202 "" 1 "" {XPPMATH -1 "6%\"\" #\"\"\"F$" }}{PARA 202 "" 1 "" {XPPMATH -1 "6$7%\"\"#\"\"\"<#-I'vector G6$I*protectedGF*I(_syslibG6\"6#7%F%\"\"!F/7%F%F$<$-F(6#7%F/F%F/-F(6#7 %F/F/F%" }}{PARA 202 "" 1 "" {XPPMATH -1 "6%\"\"\"^#F#^#!\"\"" }} {PARA 202 "" 1 "" {XPPMATH -1 "6%7%\"\"\"F$<#-I'vectorG6$I*protectedGF )I(_syslibG6\"6#7%\"\"!F.F$7%^#F$F$<#-F'6#7%F0F$F.7%^#!\"\"F$<#-F'6#7% F6F$F." }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 0 41 "#hf3/7 Rotieren um y mit 30, Proj. auf xz" }{MPLTEXT 1 0 58 "\nR3:=matrix(3,3,[sqrt(3 )/2,0,1/2,0,1,0,-1/2,0,sqrt(3)/2]);" }{MPLTEXT 1 0 36 "\nP:=matrix(3,3 ,[1,0,0,0,0,0,0,0,1]);" }{MPLTEXT 1 0 13 "\nevalm(P&*v);" }{MPLTEXT 1 0 17 "\nevalm(P&*R3&*v);" }{MPLTEXT 1 0 17 "\nevalm(R3&*P&*v);" } {MPLTEXT 1 0 13 "\nevalm(P&*P);" }{MPLTEXT 1 0 16 "\neigenvalues(P);" }{MPLTEXT 1 0 17 "\neigenvectors(P);" }{MPLTEXT 1 0 1 "\n" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#>I#R3G6\"-I'matrixG6$I*protectedGF)I(_sysli bGF%6#7%7%,$*$\"\"$#\"\"\"\"\"#F1\"\"!F17%F4F2F47%#!\"\"F3F4F." }} {PARA 202 "" 1 "" {XPPMATH -1 "6#>I\"PG6\"-I'matrixG6$I*protectedGF)I( _syslibGF%6#7%7%\"\"\"\"\"!F/7%F/F/F/7%F/F/F." }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslibG6\"6#7%\"\"\"\"\"! \"\"$" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I( _syslibG6\"6#7%,&*$\"\"$#\"\"\"\"\"#F.#F-F0F/\"\"!,&#!\"\"F0F/F,F1" }} {PARA 202 "" 1 "" {XPPMATH -1 "6#-I'vectorG6$I*protectedGF&I(_syslibG6 \"6#7%,&*$\"\"$#\"\"\"\"\"#F.#F-F0F/\"\"!,&#!\"\"F0F/F,F1" }}{PARA 202 "" 1 "" {XPPMATH -1 "6#-I'matrixG6$I*protectedGF&I(_syslibG6\"6#7% 7%\"\"\"\"\"!F-7%F-F-F-7%F-F-F," }}{PARA 202 "" 1 "" {XPPMATH -1 "6%\" \"\"F#\"\"!" }}{PARA 202 "" 1 "" {XPPMATH -1 "6$7%\"\"\"\"\"#<$-I'vect orG6$I*protectedGF*I(_syslibG6\"6#7%F$\"\"!F/-F(6#7%F/F/F$7%F/F$<#-F(6 #7%F/F$F/" }}}{EXCHG {PARA 200 "> " 0 "" }}{PARA 203 "" 0 "" }} {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }