{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 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 }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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "a := matrix(2, 4, [1,0,1,0,0 ,1,-2,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'matrixG6#7$7&\" \"\"\"\"!F*F+7&F+F*!\"#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "b := randmatrix(3, 2, entries=rand(-5..5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'matrixG6#7%7$\"\"%!\"\"7$!\"%F+7$F+F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "multiply(b,a);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7&\"\"%!\"\"\"\"'\"\"!7&!\"%F)!\"# F+7&F)F-\"\"(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "gaussjor d(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7&\"\"\"\"\"!F( F)7&F)F(!\"#F)7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "v := [ 2, -1]:\nw := [1, 5]:\npv := arrow([0,0],v,.001, .04, .04, color=red): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "pw := arrow([0,0],w,.001, .04, \+ .04, color=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "vv := arrow(v,v +w,.001, .04, .04, color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 99 " ww := arrow(w,w+v,.001, .04, .04, color=blue):\nvw := arrow([0,0],v+w, .001, .04, .04, color=green):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p lots[display](\{pv,pw,vv,ww,vw\}, axes=normal, view=[-3..7,-3..7]);" } }{PARA 13 "" 1 "" {GLPLOT2D 769 559 559 {PLOTDATA 2 "6.-%)POLYGONSG6&7 &7$$\"+yL!H!\\!#8!+bn!e!)*!#97$$!+yL!H!\\F*$\"+bn!e!)*F-7$$\"+(4(4&f* !#5\"+e!)4+[!\"*7$$\"+.H!\\g*F6$\"+U>!**z%F97%7$$\"+lQ)QS*F6\"+BB#R! [F97$$\"\"\"\"\"!$\"\"&FH7$$\"+Nh6'z*F6\"+xw2'z%F9-%&STYLEG6#%,PATCHN OGRIDG-%'COLOURG6&%RGBG\"*++++\"!\")FHFH-%'CURVESG6#7*F'F.F3F@FEFKF: F'-F6&7&7$$\"+!H!\\+?F9$!+e!)4+5F97$$\"+5(4&**>F9!+>%>!****F67$$\"+5 (4&fHF9$\"+e!)4+QF97$$\"+!H!\\gHF9\"+U>!**zF97%7$$\"+'Q)QSHF9$\"+BB# R!QF97$$\"\"FH\"\"%FH7$$\"+9;hzHF9$\"+xw2'z$F9FP-FU6&FWFHFHFX-Ffn6#7 *F\\oFaoFfoFapFfpF[qF[pF\\o-F$6&7&7$$!+xz1OAF*!+af8sWF*7$$\"+xz1OAF*$ \"+af8sWF*7$$\"+2OA?>F9!+ky_&f*F67$$\"+$Rw(>>F9$!+O@Z/'*F67%7$$\"+sU% *G>F9!+iX6@%*F67$$\"\"#FH$!\"\"FH7$$\"+Gd06>F9!+Qa))y(*F6FPFT-Ffn6#7 *FhqF]rFbrF]sFbsFgsFgrFhq-F6&7&7$$\"+KRw(***F6$\"+'y_&**\\F97$$\"+2OA +5F9\"+9sW+]F97$$\"+2OA?HF9$\"+9sWSSF97$$\"+Rw(>HF9\"+'y_&RSF97%7$$ \"+sU%*GHF9$\"+W&))y0%F9Ffp7$$\"+Gd06HF9\"+c96ASF9FPFq-Ffn6#7*FbtFgt F\\uFguFfpF\\vFauFbt-F6&7&7$$\"+++++SF*$!+++++IF*7$$!+++++SF*\"+++++ IF*7$$\"+++gzGF9$\"+++ISQF97$$\"+++S!)GF9\"+++qRQF97%7$$\"++++kGF9$\" ++++_QF9Ffp7$$\"++++'*GF9\"++++GQF9FP-FU6&FWFHFXFH-Ffn6#7*FgvF\\wFawF \\xFfpFaxFfwFgv-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6;!\"FH\"\"(FHFby" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "with(plots):\nimplicitplot(y=x, x=-5..5, y= -5..5, view=[-5..5, -5..5], scaling=CONSTRAINED);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 288 305 305 {PLOTDATA 2 "6&-%'CURVESG6U77$$!\"&\"\"!F(7$$!1+++++++[!#:F,77$$!1++ +++++YF.F1F+7$F07$$!1*************R%F.F577$$!1*************>%F.F9F47$F87$$!1**************RF.F=77$$!1*************z$F.FAF<7$F@7$$!1******* ******fF.FE77$$!1*************R$F.FIFD7$FH7$$!1*************>F.FM7 7$$!\"$F*FQFL7$FP7$$!1+++++++GF.FU77$$!1+++++++EF.FYFT7$FX7$$!1++++++ +CF.Fgn77$$!1+++++++AF.F[oFfn7$Fjn7$$!\"#F*F_o77$$!1+++++++=F.FcoF^o 7$Fbo7$$!1+++++++;F.Fgo77$$!1+++++++9F.F[pFfo7$Fjo7$$!1+++++++7F.F_p7 7$$!\"\"F*FcpF^p7$Fbp7$$!1**************z!#;Fgp77$$!1**************f FipF\\qFfp7$F[q7$$!1)*************RFipFq77$$!1)*************>FipFdqF _q7$Fcq7$$\"1p@ " 0 "" {MPLTEXT 1 0 58 "v := [3, 4]:\npv := ar row([0,0],v,.05, .2, .04, color=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plots[display](\{pv\}, axes=normal, view=[-3..7,-3..7]);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%)POLYGONSG6&7& 7$$\"+++++?!#6$!+++++:F*7$$!+++++?F*\"+++++:F*7$$\"++++gG!\"*$\"++++b QF57$$\"+++++HF5\"++++DQF57%7$$\"+++++GF5$\"+++++RF57$$\"\"\"\"!\" \"%FF7$$\"++++gHF5$\"++++!y$F5-%&STYLEG6#%,PATCHNOGRIDG-%'COLOURG6&%$R GBG$\"*++++\"!\")FFFF-%'CURVESG6#7*F'F-F2F>FCFIF8F'-%*AXESSTYLEG6#%'NO RMALG-%%VIEWG6$;$!\"$FF$\"\"(FFF^o" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "w ith(plots):\np := arrow([2,3],[-4,2],.05, .2, .04, color=red):\nq := p ointplot(\{[2,3],[-4,2]\}, symbol=circle):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots[display](\{p,q\}, axes=normal, view=[-5..5,-5.. 5]);" }}{PARA 13 "" 1 "" {GLPLOT2D 786 667 667 {PLOTDATA 2 "6'-%'CURVE SG6#7*7$$\"+D+*e*>!\"*\"+[)fY-F*7$$\"+v*4T+#F*$\"+_,MvHF*7$$!+D+*ev 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:= arrow([0,0,0],v,.15, .5, .04, color=red, \+ thickness=2):\nau := arrow([0,0,0],u,.15, .5, .04, color=red, thicknes s=2):\naunormed := arrow([0,0,0],unormed,.15, .5, .04, color=blue, thi ckness=3):\n\ndp := dotprod(unormed, v):\nproj := map(x -> x*dp, unorm ed);\nl1 := line(v, proj, thickness=2, color=green):\nplots[display]( \{av, au, aunormed, l1\}, axes=normal, view=[-3..7,-3..7, -3..7], scal ing=CONSTRAINED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%projG7%#!#g\"# \\#\"#!*F(#\"!=F(" }}{PARA 13 "" 1 "" {GLPLOT3D 931 810 810 {PLOTDATA 3 "6)-%'CURVESG6%77%\"\"!\"\"#F(\"\"%F(7%!+'z*[C7!\"*\" +%pMn=F0\"+)QpMnF0-%*THICKNESSG6#F*-%'COLOURG6&%RGBGF(\"*++++\"! \")F(-%)POLYGONSG6'7&7%F(\"+LR?3n!#6!+m>5aLFF7%F(!+LR?3nFF\"+m>5aL FF7%F(\"+hz\"H&=F0\"+?5atQF07%F(\"+R?3()>F0\"+!)*ek!QF07%7%F(\"+- KR'p\"F0\"+*R.=&RF07%F(\"+++++?F0\"+++++SF07%F(\"+)z1O9#F0\"+,m>G PF0-%&STYLEG6#%,PATCHNOGRIDG-F96&F;FF0\"+[*)[LHF0\"+4p8s&F07%7%!+sc8,=F0 \"+3Nq,FF0\"+)op())eF07%!+++++?F0\"+++++IF0\"+++++gF07%!+GV')Q?F0 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{PLOTDATA 2 "6*-%)POLYGONSG6'7&7$$!+* QRiG\"!#6$!+:BtV@F*7$$\"+*QRiG\"F*\"+:BtV@F*7$$\"+%RiG\"[!\"*$!+xEceG F57$$\"+1w8(y%F5!+BtV,HF57%7$$\"+w&\\9&[F5$!+22D%z#F57$$\"\"&\"\"!! \"FF7$$\"+C/b[ZF5$!+$H\\d'HF5-%&STYLEG6#%,PATCHNOGRIDG-%'COLOURG6&%$R GBG$\"*++++\"!\")FFFF-%*THICKNESSG6#\"\"#-%'CURVESG6#7*7$$\"+\"\\]nQ\" F*!+Od7!3#F*7$$!+\"\\]nQ\"F*$\"+Od7!3#F*7$$\"+&\\Kh'GF5\"+d7!3%>F57 \"+!)*HX#GF5\"+H]?.?F57$$\"\"$FF$FfnFF7$$\"+?+ZNHF5\"+r\\zO=F57$$\" +0v'Q*GF5$\"+V()>**=F5F[o-F$6'7&F[oFoFeoFhp7%FjoF_pFcpFNFRFY-Fhn6%7$F C7$$\"+xI#p2#F5\"+&Q:YQ\"F5-FS6&FUFFFVFFFY-Fhn6#7*F'F-F2F>FCFIF8F'-%* AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6;FG\"\"(FFF ir" 1 2 0 1 0 2 9 1 4 1 1.000000 84.000000 -5.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "with(plottools): with(linalg):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "v := [2, -1, 3]:\nw := [1, 5, -2]: \npv := arrow([0,0,0],v,.05, .2, .1, color=red, thickness=3):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "pw := arrow([0,0,0],w,.05, .2, .1, \+ color=red, thickness=3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "vv := a rrow(v,v+w,.05, .2, .1, color=blue, thickness=2):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 221 "ww := arrow(w,w+v,.05, .2, .1, color=blue, thickne ss=2):\n\ncp := crossprod(v, w):\nacp := arrow([0,0,0], cp, .1, .4, .1 , color=green, thickness=3):\npgm := polygon([[0,0,0], v,v+w,w], color =yellow, linestyle=3, thickness=1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "plots[display](\{pv,pw,vv,ww,acp,pgm\}, axes=normal, view=[-15..15 ,-15..15,-15..15]);" }}{PARA 13 "" 1 "" {GLPLOT3D 1018 877 877 {PLOTDATA 3 "6*-%)POLYGONSG6'7&7%!+EW8IE!#6\"+HiA;9F*!+ebd4SF*7%\" +EW8IEF*!+HiA;9F*\"+ebd4SF*7%!+m)pt;\"!\")\"+RxeG'!\"*\"+ed4S**F <7%!+M,js6F9\"+jA;9jF<\"+YU!*f)*F<7%7%!+i%z%f6F9\"+_4NViF<\"+-Q g+\"F97%!+++++8F9\"+++++qF<\"+++++6F97%!+Q0_!=\"F9\"+]!\\mN'F<\" +!)phR(*F<-%&STYLEG6#%,PATCHNOGRIDG-%'COLOURG6&%RGBG\"\"!\"*++++\"F9 F^o-%*THICKNESSG6#\"\"-F6'7&7%\"+H%Gz,\"F<\"+&yN5*\\F<!+e.%\\,#F< 7%\"+4dr?)*!#5\"+:U'*3]F<!+U'f])>F<7%\"+r:2#y#F<\"+:U'*3TF<\"*e. %\\rF<7%\"+H%Gz\"GF<\"+'yN54%F<\"*U'f]oF<7%7%\"+G'GGFF<\"+eo&e8% F<\"*I9wf(F<7%\"+++++IF<\"+++++SF<\"+++++5F<7%\"+kWF<!+M\\4*=F<7%\"+)*********Fbp\"+++ ++]F<!+++++?F<7%\"+'[6;2*Fbp\"+Xd!e%F<!+m]!pq\"FF<!+O9&*35F<\"+nis wHF<7%\"+8(4#)*GF<\"+l&[5\\F<\"+nisw6F<7%\"+(G!z,HF<\"+P9&*3NF< \"+LPFB7F<7%7%\"+^)QG*GF<\"+dU>kMF<\"+m]!p5\"F " 0 "" {MPLTEXT 1 0 49 "a := matrix (3, 3, [1,3/4,2/7,1,1/3,5/9,1,1/5,x]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'matrixG6#7%7%\"\"\"#\"\"\"\"%#\"\"#\"\"(7%F*#F*F,#\"\" &\"\"*7%F*#F*F4%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det( a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG#!\"&\"#7#\"P\"%g7\"\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve(%, x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"P\"D&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 489 "with(plottools): with(linalg):\nv := [1, 11]:\nu := [4, 3]:\nunormed := map(x -> x/norm(u,2), u):\n\ndp := dotprod(uno rmed, v):\nproj := map(x -> x*dp, unormed);\nl1 := arrow(proj, v, .05, .2, .04, thickness=3, color=green):\nl2 := arrow(u, proj, .05, .2, .0 4, thickness=3, color=green):\nav := arrow([0,0],v,.05, .2, .04, color =red, thickness=2):\nau := arrow([0,0],u,.05, .3, .04, color=red, thic kness=2):\nplots[display](\{l2, av, au, l1\}, axes=normal, view=[-3..1 0, -3..13], scaling=CONSTRAINED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%projG7#\"[\"\"#D#\"6\"F(" }}{PARA 13 "" 1 "" {GLPLOT2D 365 400 400 {PLOTDATA 2 "6--%)POLYGONSG6'7&7$$\"++++:S!\"*$\"++++!)HF*7$$\"+++ +&)RF*\"++++?IF*7$$\"+++?GeF*$\"+++S-WF*7$$\"+++?eeF*\"+++SiVF*7%7$$ \"+++?$y&F*$\"+++SiWF*7$$\"++++?fF*\"++++SWF*7$$\"+++?.fF*$\"+++S-VF* -%&STYLEG6#%,PATCHNOGRIDG-%'COLOURG6&%$RGBG\"\"!$\"*++++\"!\")FT-%*THI CKNESSG6#\"\"$-%'CURVESG6#7*F'F-F2F=FBFGF7F'-Fgn6#7*7$$\"+;It*[#!#6!+ ^ORjA!#77$$!+;It*[#Fo$\"+^ORjAFco7$$\"+)pE5N*!#5\"+RjAc5FW7$$\"+%z1T g)F\\p$\"+d!p0\"FW7$$\"\"\"FT\"#6FT7$$\"+@$*ef5F*$\"+VY4b5FW7$$\"+-L (*[)*F\\p\"+hOxb5FWF]o-F6'7&F]oFdoFioF^q7%F_pFdpFipFL-FQ6&FSFUFTFT-F Y6#\"\"#-Fgn6#7*7$$\"++++SfF*$\"++++bWF*7$$\"+++++fF*\"++++DWF*7$$\"+ ++!o<\"F*$\"+++Es5FW7$$\"+++!o6\"F*\"+++wn5FWFdp7$$\"+++!oF\"F*$\"+++ wz5FW7$$\"+++!o@\"F*\"+++Ev5FWF_r-F6'7&F_rFdrFirFhs7%F^sFdpFcsFLFPFX -F6'7&7$$\"+++++:Fo$!+++++?Fo7$$!+++++:Fo\"+++++?Fo7$$\"++++DQF* $\"+++++HF*7$$\"++++bQF*\"++++gGF*7%7$$\"++++]PF*$FenFT7$$\"\"%FTF\\v 7$$\"++++IRF*$\"++++gFF*FLFgqFiq-Fgn6#7*FdtFitF^uFiuF]vFvFcuFdt-%*AXE SSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;$!\"$FT$\"#5FT ;Fdw$\"#8FT" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }} {TEXT -1 3 "det" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "a := mat rix(4, 4, [1, 12, 1, 2, 1, 20, -1,3,1,-3,4,-1,1,-3,6,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'matrixG6#7&7&\"\"\"\"#7F*\"\"#7&F*\"#? !\"\"\"\"$7&F*!\"$\"\"%F/7&F*F2\"\"'F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 188 "with(linalg):\na := vector( [10,0,0]):\nb := vector([8,5,0]):\nc := vector([5,3,5]):\nnorm(crosspr od(a, b),2) + norm(crossprod(a, c),2) + norm(crossprod(b, c),2)\n+ nor m(crossprod(b-a, c-a),2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"#]\" \"\"*$-%%sqrtG6#\"#M\"\"\"\"#5*$-F(6#\"%EAF+F%*$-F(6#\"%'3\"F+F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "map(evalf, op(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$\"#]\"\"!$\"+&*=&4$e!\")$\"+X/0=ZF($\"+69X& H\$F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?ops" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "13 6 0" 2 }{VIEWOPTS 1 1 0 1 1 1803 }