{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 }{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 Outpu t" 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 "" 0 256 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 }{PSTYLE "" 0 257 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 "" {TEXT -1 24 "Matrix Algebra example 1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "To find the equilibrium points of the system" }}{PARA 256 "" 0 "" {OLE 1 4097 1 "[xm]Br=WfoRrB:::wk;nyyI;G:;:j::>:B>N:F:nyyyyy]::yyyyyy:::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::fyyyyya :nYf::G:jy;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::JcvGYMt>^:fBWMtNHm=;:::::::n:;JZC:bK B::>hf>]]OkRpq;V:>j>Z:j:vCSmlJ::::::::::OJ;@jyyyyyy;jysy;Z:::::::^<>:F ::]KRnC=MtFGgml>:;::::::JGN:ry:>:<::::::=J:>K>:F:AlqfG[maNFO=;:::::::: _J;vyyuy:>:<::::::AZ:^E>:nYN:JZ:>;;J?>:wAQ:S:UJ:n;v;;JBCR:HjklN\\=@iAFX?:D=D;;B:xIyA;Z:vYxI:J:B:::::=Jyyy;d:yayY;A: ;JZC:bK_J:fc[_hb_ds?h_?^?GhoGfnGgioGM:ETV:::^xsNpkK:<::::::::yayY:^Z:j :>:yayQ:>:fxBjQM:gh:D:;B:CZ:NZ;F:E:=b:yyyyI:E:M:;:;q@[;;B:::::::JFNZ;J:N:;B:yayA:;B::::::f:=;jysy:>:<::::::wyyyA<::::::::::::jysy:>:<:::: :::::::::::::::vYxI:;Z:::::::::]:qi:;fy>Z:JBAJ:UDO;SKkEW_URPM< jP@:MB:;B:_c::::::::::_kf<l ;F:>Zx;j>>:_kb@J`F:o:F;N@>g=F:;J vJ?B:_;uc;?:kUXKONG;N@]v:kl:jv>OJSjDIj:<:kE:N;N@Nj@N:>is;[B:X=j>>:_c<]Lh@j:>Z:fAkp>JSjjLj:>:QKf;_kB?g;F:fA :_;wf:=J:f_:>UJSJAMj:jOjD>:qAB:>l;Z:b:^DP@::C:US:=JZ: B:;p>ZDjuPj:jS>RJSFLCW;=:<:O:Gc;N;yyyxy:J:><:B>N:F:nyyyyy]::yyyyyy:::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::fyyyyya :nYf::G:jy;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::JcvGYMt>^:fBWMtNHm=;:::::::n:;JZC:bK B::>\\mH]]OkRpq;V:>r>Z:j:vCSmlJ::::::::::OJ;@jyyyyyy;jysy;Z:::::::^<>: F::]KRnC=MtFGgml>:;::::::JGN:ry:>:<::::::=J:>J<:F:AlqfG[maNFO=;::::::: :_J;vyyuy:>:<::::::?J:j;B:wAE:G:IZ:F;nYN;V;;J@>:UJ:n;v;;JB@]K]V@]KU>Au=[D:=mkVG=mmfFs=CR:HjklN\\=@iAVX?b[Q[lF:wyy AbR<:TNC>:UTRcETcTX[US;SK]UW=EWMuUWm>j\\@A:::cYH_WV>Z::JR> @=lZ>@[kRFB]KUf@_kxJbjnnGyyyxy;B:CB:F:vYxY;J:jt]:YG;^a=j:F;HJIA:?JHB:; j;>ryysyAvAv[>V;n>^;UTRZ_?Z:>VEZ:F;B:sZ:Vy<>jxM:<:[V:;B: DJ:DJ:=?R:J;>:yayA:;B::::::^:;B:gu:Z:v YxI:;Z::::::JywYB:::::::::::::yay=J:B:::::::::::::::::::jysy:>:<:::::: ::_rZkm;?Z:>Z:j;@JHYJ;fEAR:ay;?JkVZ;FsAN:wL:>:::::f_;j>H=B:< JM`Q:G;N@Ev:gm:B:G;s:qQ:[:JBAj:B:;b:JSJnHj:>:k=OJ:Z:>INOM:_kBIJfF :FisOOM:_;=w:=:m=O:_;Wf;?:k=OOHjw;<:[V:;ZX=j>>Z:N`DFDsT:=J:F:;jO`qc;_kB?g;F:fA:_;wf: =J:f_sWTJSJGMj:<:Q;sZ:VYZ:JBA::Gc;N;yyyxy:J:^=VY[j=J:^q:I:J:C:[q:VZ:B:;::::::::jysy:>:<:::::::::::: :::::::vYxI:;Z::::::::::::::::::::yay=J:B:::::5:" }{TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "To find t he equilibrium point. First load the package 'linalg'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Then enter the equations as follows" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "A:=2*x+3*x*y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "B:=-y+2*x*y;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "At the equilibrium point A=B=0" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Now use the 'solve' command to sol ve the simultaneous equations " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(\{A=0,B=0\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }