{VERSION 4 0 "HP RISC UNIX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple O utput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "He lvetica" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 52 "Themenvorschl\344ge zu d en \334bungen am 27./28. Mai 2002 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "restart: with(linalg): \nA := matrix([[1/(i+j) $i=1..3] $j=1..3]);" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been redefined and unprotected\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG 6#7%7%#\"\"\"\"\"##F+\"\"$#F+\"\"%7%F-F/#F+\"\"&7%F/F2#F+\"\"'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M := concat(A, diag(1$3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7%7(#\"\"\"\"\"##F +\"\"$#F+\"\"%F+\"\"!F17(F-F/#F+\"\"&F1F+F17(F/F3#F+\"\"'F1F1F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "M1 := addrow(M, 1, 2, -2/3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M1G-%'matrixG6#7%7(#\"\"\"\"\"# #F+\"\"$#F+\"\"%F+\"\"!F17(F1#F+\"#O#F+\"#I#!\"#F.F+F17(F/#F+\"\"&#F+ \"\"'F1F1F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "M2 := addrow (M1, 1, 3, -1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M2G-%'matrixG6 #7%7(#\"\"\"\"\"##F+\"\"$#F+\"\"%F+\"\"!F17(F1#F+\"#O#F+\"#I#!\"#F.F+F 17(F1F5#F+\"#C#!\"\"F,F1F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "M3 := addrow(M2, 2, 3, -6/5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#M3G-%'matrixG6#7%7(#\"\"\"\"\"##F+\"\"$#F+\"\"%F+\"\"!F17(F1#F+\"#O# F+\"#I#!\"#F.F+F17(F1F1#F+\"$+'#F.\"#5#!\"'\"\"&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "L := delcols(M3, 1..3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"LG-%'matrixG6#7%7%\"\"\"\"\"!F+7%#!\"#\"\"$F*F+7% #F/\"#5#!\"'\"\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "R := delcols(M3, 4..6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'matrix G6#7%7%#\"\"\"\"\"##F+\"\"$#F+\"\"%7%\"\"!#F+\"#O#F+\"#I7%F2F2#F+\"$+' " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(L &* A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' matrixG6#7%7%#\"\"\"\"\"##F)\"\"$#F)\"\"%7%\"\"!#F)\"#O#F)\"#I7%F0F0#F )\"$+'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "b) " }{XPPEDIT 18 0 "A \+ = L^(-1)*R;" "6#/%\"AG*&)%\"LG,$\"\"\"!\"\"F)%\"RGF)" }{TEXT -1 19 "; \+ wir m\374ssen also " }{XPPEDIT 18 0 "L;" "6#%\"LG" }{TEXT -1 13 " inv ertieren:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M := concat(L, diag(1$3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7%7( \"\"\"\"\"!F+F*F+F+7(#!\"#\"\"$F*F+F+F*F+7(#F/\"#5#!\"'\"\"&F*F+F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "M1 := addrow(M, 1, 2, 2/3 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M1G-%'matrixG6#7%7(\"\"\"\"\" !F+F*F+F+7(F+F*F+#\"\"#\"\"$F*F+7(#F/\"#5#!\"'\"\"&F*F+F+F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "M2 := addrow(M1, 1, 3, -3/10 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M2G-%'matrixG6#7%7(\"\"\"\"\" !F+F*F+F+7(F+F*F+#\"\"#\"\"$F*F+7(F+#!\"'\"\"&F*#!\"$\"#5F+F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "M3 := addrow(M2, 2, 3, 6/5); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M3G-%'matrixG6#7%7(\"\"\"\"\"!F +F*F+F+7(F+F*F+#\"\"#\"\"$F*F+7(F+F+F*#F*F.#\"\"'\"\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Linvers := delcols(M3, 1..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%(LinversG-%'matrixG6#7%7%\"\"\"\"\"! F+7%#\"\"#\"\"$F*F+7%#F*F.#\"\"'\"\"&F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm(L &* Li nvers);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\"\"\"! F)7%F)F(F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm (Linvers &* R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%#\" \"\"\"\"##F)\"\"$#F)\"\"%7%F+F-#F)\"\"&7%F-F0#F)\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "c) Wegen b) ist " }{XPPEDIT 18 0 "A^(-1) = R^(-1)*L;" "6#/)%\"AG,$\"\"\"!\"\"*&)%\"RG,$F'F(F'%\"LGF'" }{TEXT -1 20 " . Wir m\374ssen also " }{XPPEDIT 18 0 "R;" "6#%\"RG" }{TEXT -1 13 " invertieren:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "M := concat (R, diag(1$3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7 %7(#\"\"\"\"\"##F+\"\"$#F+\"\"%F+\"\"!F17(F1#F+\"#O#F+\"#IF1F+F17(F1F1 #F+\"$+'F1F1F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "M1 := add row(M, 3, 2, -20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M1G-%'matrixG 6#7%7(#\"\"\"\"\"##F+\"\"$#F+\"\"%F+\"\"!F17(F1#F+\"#OF1F1F+!#?7(F1F1# F+\"$+'F1F1F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "M2 := addr ow(M1, 3, 1, -150);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M2G-%'matrix G6#7%7(#\"\"\"\"\"##F+\"\"$\"\"!F+F/!$]\"7(F/#F+\"#OF/F/F+!#?7(F/F/#F+ \"$+'F/F/F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "M3 := addrow (M2, 2, 1, -12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M3G-%'matrixG6# 7%7(#\"\"\"\"\"#\"\"!F-F+!#7\"#!*7(F-#F+\"#OF-F-F+!#?7(F-F-#F+\"$+'F-F -F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "M4 := mulrow(M3, 1, \+ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M4G-%'matrixG6#7%7(\"\"\"\" \"!F+\"\"#!#C\"$!=7(F+#F*\"#OF+F+F*!#?7(F+F+#F*\"$+'F+F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "M5 := mulrow(M4, 2, 36);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M5G-%'matrixG6#7%7(\"\"\"\"\"!F+\"\"#!#C \"$!=7(F+F*F+F+\"#O!$?(7(F+F+#F*\"$+'F+F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "M6 := mulrow(M5, 3, 600);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M6G-%'matrixG6#7%7(\"\"\"\"\"!F+\"\"#!#C\"$!=7(F+F*F +F+\"#O!$?(7(F+F+F*F+F+\"$+'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Rinvers := delcols(M6, 1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%(RinversG-%'matrixG6#7%7%\"\"#!#C\"$!=7%\"\"!\"#O!$?(7%F.F.\"$+'" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm(R &* Rinvers);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\"\"\"!F)7%F)F(F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Ainvers := evalm(Rinvers &* L);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%(AinversG-%'matrixG6#7%7%\"#s!$S#\"$!=7%F+\"$+ *!$?(7%F,F/\"$+'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm(A &* Ainvers);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\"\"\"!F)7%F)F(F)7%F)F)F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "d) " }{TEXT 256 97 "(kann am Mont ag noch nicht gemacht werden, da der Multiplikationssatz erst am Diens tag drankommt)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"&+K%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"&+ K%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "R[1,1] * R[2,2] * R[3 ,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"&+K%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "e) Schreibe um durch Multiplikation mit \+ " }{XPPEDIT 18 0 "L;" "6#%\"LG" }{TEXT -1 1 ":" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Links := evalm(R &* [x, y, z]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&LinksG-%'vectorG6#7%,(%\"xG#\"\"\" \"\"#*&#F,\"\"$F,%\"yGF,F,*&#F,\"\"%F,%\"zGF,F,,&F1#F,\"#O*&#F,\"#IF,F 5F,F,,$F5#F,\"$+'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Rechts := evalm(L &* [a, b, c]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Recht sG-%'vectorG6#7%%\"aG,&F)#!\"#\"\"$%\"bG\"\"\",(F)#F-\"#5*&#\"\"'\"\"& F/F.F/!\"\"%\"cGF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "LGSne u := seq(Links[i] = Rechts[i], i=1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'LGSneuG6%/,(%\"xG#\"\"\"\"\"#*&#F*\"\"$F*%\"yGF*F**&#F*\"\"%F *%\"zGF*F*%\"aG/,&F/#F*\"#O*&#F*\"#IF*F3F*F*,&F4#!\"#F.%\"bGF*/,$F3#F* \"$+',(F4#F.\"#5*&#\"\"'\"\"&F*F?F*!\"\"%\"cGF*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "solve(\{LGSneu\}, \{x,y,z\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"xG,(%\"aG\"#s*&\"$S#\"\"\"%\"bGF+!\"\"*&\"$! =F+%\"cGF+F+/%\"yG,(F'!$S#*&\"$+*F+F,F+F+*&\"$?(F+F0F+F-/%\"zG,(F'F/*& F8F+F,F+F-*&\"$+'F+F0F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "f)" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "v := [1,0,1]; w := [1,1,0];\ndotpr od(v, w) mod 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"\"\"\"! F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG7%\"\"\"F&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "crossprod(v, w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'vectorG6#7%!\"\"\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "map(modp, crossprod(v, w), 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'vectorG6#7%\"\"\"F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 315 "g) E in Dreieck ist ein halbes Parallelogramm\nh) Die Grundfl\344che ist da s halbe Vektorprodukt zweier Kanten. Zweimal Grundfl\344che mal Hoehe \+ ist der Betrag des Spatprodukts dreier Kanten, das Volumen des Tetraed ers also 1/6 mal dem Spatprodukt der Vektoren AB, AC und AD.\ni) Offen sichtlich sind alle Kantenl\344ngen gleich" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "assume(a > 0): sqrt(a^2 + a^2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*&-%%sqrtG6#\"\"#\"\"\"%#a|irGF(" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 2 "j)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "unprotect( D):\nA := [a,0,0]: B := [0,a,0]: C := [0,0,a]: D := [a,a,a]:\nv := cro ssprod(B-A, C-A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6 #7%*$)%#a|irG\"\"#\"\"\"F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Spatprod := dotprod(v, D-A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%)SpatprodG,$*$)%#a|irG\"\"$\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Volumen := Spatprod/6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(VolumenG,$*$)%#a|irG\"\"$\"\"\"#F*F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "In Abh\344ngigkeit von s:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(a = s/sqrt(2), Volumen);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%\"sG\"\"$\"\"\"-%%sqrtG6#\"\"#F(#F(\"#7" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "k) 0, da der Spaltenrang der Matri x nur zwei ist.\nl)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "y := [1,3,5, 2,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG7'\"\"\"\"\"$\"\"&\"\"# \"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "i :='i': pi := [[i , y[i]] $ i=1..5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#piG7'7$\"\"\" F'7$\"\"#\"\"$7$F*\"\"&7$\"\"%F)7$F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "InverseOrdnung := (x, y) -> evalb(x[2] < y[2]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%/InverseOrdnungGR6$%\"xG%\"yG6\"6$%) operatorG%&arrowGF)-%&evalbG6#2&9$6#\"\"#&9%F3F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "pi1 := sort(pi, InverseOrdnung);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pi1G7'7$\"\"\"F'7$\"\"%\"\"#7$F*\" \"$7$\"\"&F)7$F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "matri x([[i$i=1..5],[%[i][1] $ i=1..5]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7$7'\"\"\"\"\"#\"\"$\"\"%\"\"&7'F(F+F)F,F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "m) Schreibe zun\344chst als Produkt eleme ntfremder Zykeln:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(group): c onvert(y, 'disjcyc');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7&\"\"#\"\" $\"\"&\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Also nur ein Zyklu s, der leicht als Produkt von Transpositionen geschrieben werden kann: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mulperms([[2,4]],[[3,4]]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7#7%\"\"#\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "mulperms(%, [[5,4]]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7#7&\"\"#\"\"$\"\"&\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "n) ungerade, da Produkt von drei Transpositionen.\no)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "A := matrix(5,5,[0$25]):\nfor i to \+ 5 do A[i, y[i]] := 1 od:\nevalm(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7'7'\"\"\"\"\"!F)F)F)7'F)F)F(F)F)7'F)F)F)F)F(7'F)F(F)F)F) 7'F)F)F)F(F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "for i to 5 do \nBild([0$(i-1), 1, 0$(5-i)]) =\nevalm(A &* [0$(i-1), 1, 0$(5-i)]) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%BildG6#7'\"\"\"\"\"!F)F)F)-%'vectorGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%BildG6#7'\"\"!\"\"\"F(F(F(-%'vectorG6#7'F(F (F(F)F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%BildG6#7'\"\"!F(\"\"\"F (F(-%'vectorG6#7'F(F)F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%Bil dG6#7'\"\"!F(F(\"\"\"F(-%'vectorG6#7'F(F(F(F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%BildG6#7'\"\"!F(F(F(\"\"\"-%'vectorG6#7'F(F(F)F(F( " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "p) signum(" }{XPPEDIT 18 0 "P i;" "6#%#PiG" }{TEXT -1 9 ")\nq) z.B." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mulperms([[1,3]],[[2,3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7# 7%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Genauso bei variablen Eintr\344gen, aber da streikt mulperms." }}}}{MARK "1 1 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }