{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 1 }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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Helvetica" 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 57 "Rechenergebnisse zu den \nThemenvorschl\344gen f\374r den 20. Mai" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart: with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "f)" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A := matrix(3,3,[1,2,3,2,0,4,3,4,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%F+\"\"!\"\"%7%F ,F/\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "B := matrix(3,2 ,[6,10,10,10,10,22]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matr ixG6#7%7$\"\"'\"#57$F+F+7$F+\"#A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "evalm(inverse(A) &* B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7$#\"\"\"\"\"$F*7$#!\"#F*\"\"#7$#\"\"(F*F)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "g)" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "A := matrix([[1,2,3,4],[0,1,2,3],[0,0,1,2],[0 $3,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\" \"\"\"#\"\"$\"\"%7&\"\"!F*F+F,7&F/F/F*F+7&F/F/F/F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"!\"#F(\"\"!7&F*F(F)F(7&F*F*F(F)7&F*F*F*F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "B := matrix(3,3,[1,2,1, 3,lambda,2,1,3,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrix G6#7%7%\"\"\"\"\"#F*7%\"\"$%'lambdaGF+7%F*F-F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "inverse(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%'matrixG6#7%7%,&%'lambdaG\"\"\"\"\"'!\"\"F*,&\"\"%F*F)F,7%F,\"\"!F* 7%,&F)F,\"\"*F*F,F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "h) + i)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A := matrix(3,3,[-1,a,b,0,c,d,0,0,- 1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%!\"\"%\" aG%\"bG7%\"\"!%\"cG%\"dG7%F.F.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'mat rixG6#7%7%!\"\"*&%\"aG\"\"\"%\"cGF(,$*&,&*&F*F+%\"dGF+F(*&%\"bGF+F,F+F +F+F,F(F(7%\"\"!*&F+F+F,F(*&F1F+F,F(7%F5F5F(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 7 "j) + k)" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "LGS := \{a * lambda = -b, b*lambda = a\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$LGSG<$/*&%\"aG\"\"\"%'lambdaGF),$%\"bG!\" \"/*&F,F)F*F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(LG S, \{lambda, a, b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<%/%\"aG\"\"! /%\"bGF&/%'lambdaGF*<%/F%*&F(\"\"\"-%'RootOfG6$,&*$)%#_ZG\"\"#F.F.F.F. /%&labelG%$_L1GF./F*F//F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "m) 1. L\366sungsweg" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A := matrix([[ -2,2],[-21,11]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6 #7$7$!\"#\"\"#7$!#@\"#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " evalm(A &* [1,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$\" \"%\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "4 * [1,3];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"%\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm(A &* [2,7]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$\"#5\"#N" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "5 * [2,7];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"#5\"#N" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diag(4,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"%\"\"!7$F)\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "2. L\366sungsweg" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "B := matrix([[1,2],[3,7]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7$7$\"\"\"\"\"#7$\"\"$\"\"(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"(!\"#7$!\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "evalm(inverse(B) &* A &* B);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"%\"\"!7$F)\"\"&" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "M := matrix([[1,0$3],[0,1, 0,0],[-1,0,2,0],[0,-3,0,4]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"M G-%'matrixG6#7&7&\"\"\"\"\"!F+F+7&F+F*F+F+7&!\"\"F+\"\"#F+7&F+!\"$F+\" \"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "B := transpose(M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7&\"\"\"\"\"!!\" \"F+7&F+F*F+!\"$7&F+F+\"\"#F+7&F+F+F+\"\"%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "A := inverse(transpose(M));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"\"\"\"!#F*\"\"#F+7&F+F*F+#\" \"$\"\"%7&F+F+F,F+7&F+F+F+#F*F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Probe:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "for i from 0 to 3 do\nT[i] := orthopoly[T](i, x)\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"TG6#\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>&%\"TG6#\"\"\"%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"TG6#\"\" #,&*$)%\"xGF'\"\"\"F'F,!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"T G6#\"\"$,&*$)%\"xGF'\"\"\"\"\"%*&F'F,F+F,!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 34 "b := evalm(A &* [a0, a1, a2, a3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7&,&%#a0G\"\"\"*&#F+\"\"#F +%#a2GF+F+,&%#a1GF+*&#\"\"$\"\"%F+%#a3GF+F+,$F/F-,$F6#F+F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "collect(sum(b['j'+1]*T['j'], 'j'=0. .3), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&%#a3G\"\"\")%\"xG\"\"$ F&F&*&%#a2GF&)F(\"\"#F&F&*&%#a1GF&F(F&F&%#a0GF&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 34 "a := evalm(B &* [b0, b1, b2, b3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'vectorG6#7&,&%#b0G\"\"\"%#b2G!\"\", &%#b1GF+*&\"\"$F+%#b3GF+F-,$F,\"\"#,$F2\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "sum(b||(0..3)[j+1]*'''T[j]''', j=0..3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,**&%#b0G\"\"\".&%\"TG6#\"\"!F&F&*&%#b 1GF&.&F)6#F&F&F&*&%#b2GF&.&F)6#\"\"#F&F&*&%#b3GF&.&F)6#\"\"$F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "collect(eval(%), x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&%#b3G\"\"\")%\"xG\"\"$F&\"\"%*(\" \"#F&%#b2GF&)F(F,F&F&*&,&%#b1GF&*&F)F&F%F&!\"\"F&F(F&F&%#b0GF&F-F3" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum(a[j+1]*x^j, j=0..3);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&%#b3G\"\"\")%\"xG\"\"$F&\"\"%*(\" \"#F&%#b2GF&)F(F,F&F&*&,&%#b1GF&*&F)F&F%F&!\"\"F&F(F&F&%#b0GF&F-F3" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5 1 0" 18 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }