{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$$\"+Nh6'z*F6$\"+xw2'z%F9-%&STYLEG6#%,PATCHN OGRIDG-%'COLOURG6&%$RGBG$\"*++++\"!\")FHFH-%'CURVESG6#7*F'F.F3F@FEFKF: F'-F$6&7&7$$\"+!H!\\+?F9$!+e!)4+5F97$$\"+5(4&**>F9$!+>%>!****F67$$\"+5 (4&fHF9$\"+e!)4+QF97$$\"+!H!\\gHF9$\"+U>!**z$F97%7$$\"+'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$$\"+Gd06>F9$!+Qa))y(*F6FPFT-Ffn6#7 *FhqF]rFbrF]sFbsFgsFgrFhq-F$6&7&7$$\"+KRw(***F6$\"+'y_&**\\F97$$\"+2OA +5F9$\"+9sW+]F97$$\"+2OA?HF9$\"+9sWSSF97$$\"+$Rw(>HF9$\"+'y_&RSF97%7$$ \"+sU%*GHF9$\"+W&))y0%F9Ffp7$$\"+Gd06HF9$\"+c96ASF9FPF`q-Ffn6#7*FbtFgt F\\uFguFfpF\\vFauFbt-F$6&7&7$$\"+++++SF*$!+++++IF*7$$!+++++SF*$\"+++++ IF*7$$\"+++gzGF9$\"+++ISQF97$$\"+++S!)GF9$\"+++qRQF97%7$$\"++++kGF9$\" ++++_QF9Ffp7$$\"++++'*GF9$\"++++GQF9FP-FU6&FWFHFXFH-Ffn6#7*FgvF\\wFawF \\xFfpFaxFfwFgv-%*AXESSTYLEG6#%'NORMALG-%%VIEWG6$;$!\"$FH$\"\"(FHFby" 1 2 0 1 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "with(plots):\nimplicitplot(y=x, x=-5..5, y= -5..5, view=[-5..5, -5..5], scaling=CONSTRAINED);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 288 305 305 {PLOTDATA 2 "6&-%'CURVESG6U7$7$$!\"&\"\"!F(7$$!1+++++++[!#:F,7$7$$!1++ +++++YF.F1F+7$F07$$!1*************R%F.F57$7$$!1*************>%F.F9F47$ F87$$!1**************RF.F=7$7$$!1*************z$F.FAF<7$F@7$$!1******* ******f$F.FE7$7$$!1*************R$F.FIFD7$FH7$$!1*************>$F.FM7$ 7$$!\"$F*FQFL7$FP7$$!1+++++++GF.FU7$7$$!1+++++++EF.FYFT7$FX7$$!1++++++ +CF.Fgn7$7$$!1+++++++AF.F[oFfn7$Fjn7$$!\"#F*F_o7$7$$!1+++++++=F.FcoF^o 7$Fbo7$$!1+++++++;F.Fgo7$7$$!1+++++++9F.F[pFfo7$Fjo7$$!1+++++++7F.F_p7 $7$$!\"\"F*FcpF^p7$Fbp7$$!1**************z!#;Fgp7$7$$!1**************f FipF\\qFfp7$F[q7$$!1)*************RFipF`q7$7$$!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$$!+D+*ev$ F*$\"+_,M:?F*7$$!+,,cVPF*$\"+31OT>F*7$$!\"%\"\"!$\"\"#F?7$$!+**)Rkx$F* $\"+#RR'Q@F*7$$!+v*4Tw$F*$\"+[)fY1#F*F'-%)POLYGONSG6&7&F'F-F2FG7%F7F " 0 "" {MPLTEXT 1 0 273 "with(plotto ols):\nv := [3, -1, 2]:\npv := arrow([0,0,0],v,.15, .5, .04, color=red , thickness=2):\nl1 := line(v, [v[1],v[2],0], thickness=3, color=blue) :\nl2 := line([0,0,0],[v[1],v[2],0],thickness=2, color=green):\nl3 := \+ line([v[1],0,0],[v[1],v[2],0], thickness=2, color=green):" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 73 "plots[display](\{pv, l1, l2, l3\}, axes=norm al, view=[-3..7,-3..7, -3..7]);" }}{PARA 13 "" 1 "" {GLPLOT3D 1055 882 882 {PLOTDATA 3 "6(-%)POLYGONSG6'7&7%$\"+YT>.Q!#6$!+#QJxE\"F*$!+6p lQjF*7%$!+YT>.QF*$\"+#QJxE\"F*$\"+6plQjF*7%$\"+f!o>%G!\"*$!+joAt%*!#5$ \"+plQ$)>F97%$\"+T>.=HF9$!+RJxE(*F<$\"+JMhc=F97%7%$\"+ioA`FF9$!+uGUx\" *F<$\"+k&)GJ@F97%$\"+++++IF9$!+++++5F9$\"+++++?F97%$\"+QJx1IF9$!+8xD-5 F9$\"+O9r3 " 0 "" {MPLTEXT 1 0 502 "with(plot tools): with(linalg):\nv := [0,2,4]:\nu := [-2,3,6]:\nunormed := map( x -> x/norm(u,2), u):\nav := 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%7$7%\"\"!$\"\"#F($\"\"%F(7%$!+'z*[C7!\"*$\" +%pMn$=F0$\"+)QpMn$F0-%*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 $\"+#\\'HeIF0$\"+7.BJcF0FboFfoF5-F@6'7&7%F\\pF^p$!+a14jQFF7%FcpFep$\"+ a14jQFF7%$!+gTE'Q#!#5$\"+SiRzNFis$\"+$\\!)[h)Fis7%$!+E,X*4$Fis$\"+!>v \"\\YFis$\"+jBEUyFis7%7%$!+lQ@a:Fis$\"+)z?8L#Fis$\"+8$oi^*Fis7%$!+dG9d GFis$\"+'G9dG%Fis$\"+r&G9d)Fis7%$!+@/]JRFis$\"+K1D(*eFis$\"+VX(3%pFisF bo-F96&F;F(F(F<-F66#\"\"$-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTR AINEDG-%%VIEWG6%;$!\"$F($\"\"(F(F[wF[w" 1 2 0 1 0 2 1 1 4 1 1.000000 82.000000 -116.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 405 "with(plottools): with(linalg):\nv := [5, -3]:\nu := [3,2]:\nunormed \+ := map(x -> x/norm(u,2), u):\nav := arrow([0,0],v,.05, .2, .04, color= red, thickness=2):\nau := arrow([0,0],u,.05, .2, .04, color=red, thick ness=2):\n\ndp := dotprod(unormed, v):\nproj := map(x -> x*dp, unormed );\nl1 := line(v, proj, thickness=2, color=green):\nplots[display](\{a v, au, l1\}, axes=normal, view=[-3..7, -3..7], scaling=CONSTRAINED);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%projG7$#\"#F\"#8#\"#=F(" }}{PARA 13 "" 1 "" {GLPLOT2D 727 538 538 {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$6'7&F[oF`oFeoFhp7%FjoF_pFcpFNFRFY-Fhn6%7$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;\"!\")$\"+Rx$eG'!\"*$\"+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#\"\"$-F$6'7&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*[#F`o$\"+^ORjAFco7$$\"+)pE5N*!#5$\"+RjAc5FW7$$\"+%z1T g)F\\p$\"+d`!p0\"FW7$$\"\"\"FT$\"#6FT7$$\"+@$*ef5F*$\"+VY4b5FW7$$\"+-L (*[)*F\\p$\"+hOxb5FWF]o-F$6'7&F]oFdoFioF^q7%F_pFdpFipFL-FQ6&FSFUFTFT-F Y6#\"\"#-Fgn6#7*7$$\"++++SfF*$\"++++bWF*7$$\"+++++fF*$\"++++DWF*7$$\"+ ++!o<\"F*$\"+++Es5FW7$$\"+++!o6\"F*$\"+++wn5FWFdp7$$\"+++!oF\"F*$\"+++ wz5FW7$$\"+++!o@\"F*$\"+++Ev5FWF_r-F$6'7&F_rFdrFirFhs7%F^sFdpFcsFLFPFX -F$6'7&7$$\"+++++:F`o$!+++++?F`o7$$!+++++:F`o$\"+++++?F`o7$$\"++++DQF* $\"+++++HF*7$$\"++++bQF*$\"++++gGF*7%7$$\"++++]PF*$FenFT7$$\"\"%FTF\\v 7$$\"++++IRF*$\"++++gFF*FLFgqFiq-Fgn6#7*FdtFitF^uFiuF]vF`vFcuFdt-%*AXE SSTYLEG6#%'NORMALG-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;$!\"$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 }