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{TEXT 211 108 "I n this worksheet you will see some example of how to write and solve l inear systems with the Maple package." }}{PARA 0 "" 0 "" {TEXT 206 9 " Example 1" }{TEXT 211 53 ". We solve the following system of linear eq uations: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "solve(\{3*x+y- z=1,2*x+5*y+2*z=3\},\{x,y,z\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 27 "Let us try another example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{x+y=1,2*x+2*y=3\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 375 "It looks like Maple does not want to solve it. Does th at mean anything? It is a simple system: we can see that the two equat ions have proportional coefficients, however, the right hand side of t he equations are not proportional with the same constant, so the syste m is inconsistent. Let's see what we get if we use the elimnation meho d. We will use matrix notation this time." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "A:=<<1,2>|<1,2>>;# the coefficient matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "b:=<<1,3>>;# the right hand side of the equations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ReducedRo wEchelonForm();" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 145 "Now, if we look at the reduced row echaon form of the augmented matrix ( ) we see that the second row corresponds to an equation of the form " }{XPPEDIT 18 0 "Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"tru e\", executable = \"true\", font_style_name = \"2D Input\", mathvarian t = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"tr ue\", executable = \"true\", font_style_name = \"2D Input\", mathvaria nt = \"italic\"), Typesetting:-mrow(Typesetting:-mi(\"\", italic = \"t rue\", executable = \"true\", font_style_name = \"2D Input\", mathvari ant = \"italic\"), Typesetting:-mrow(Typesetting:-mn(\"0\", mathvarian t = \"normal\"), Typesetting:-mo(\"⁢\", mathvariant = \+ \"normal\", fence = \"false\", separator = \"false\", stretchy = \"fal se\", symmetric = \"false\", largeop = \"false\", movablelimits = \"fa lse\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Ty pesetting:-mi(\"x\", italic = \"true\", mathvariant = \"italic\")), Ty pesetting:-mo(\"+\", mathvariant = \"normal\", fence = \"false\", sepa rator = \"false\", stretchy = \"false\", symmetric = \"false\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.2222222em\", rspace = \"0.2222222em\"), Typesetting:-mrow(Typeset ting:-mn(\"0\", mathvariant = \"normal\"), Typesetting:-mo(\"&Invisibl eTimes;\", mathvariant = \"normal\", fence = \"false\", separator = \" false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fals e\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\" , rspace = \"0.0em\"), Typesetting:-mi(\"y\", italic = \"true\", mathv ariant = \"italic\")), Typesetting:-mi(\"\", italic = \"true\", execut able = \"true\", font_style_name = \"2D Input\", mathvariant = \"itali c\")), Typesetting:-mo(\"=\", mathvariant = \"normal\", fence = \"fals e\", separator = \"false\", stretchy = \"false\", symmetric = \"false \", largeop = \"false\", movablelimits = \"false\", accent = \"false\" , lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mn (\"1\", mathvariant = \"normal\")), Typesetting:-mi(\"\", italic = \"t rue\", executable = \"true\", font_style_name = \"2D Input\", mathvari ant = \"italic\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysl ibGF'6%-I#miGF$6'Q!F'/%'italicGQ%trueF'/%+executableGF1/%0font_style_n ameGQ)2D~InputF'/%,mathvariantGQ'italicF'-F#6&F+-F#6'F+-F#6%-I#mnGF$6$ Q\"0F'/F8Q'normalF'-I#moGF$6-Q1⁢F'FD/%&fenceGQ&falseF'/ %*separatorGFL/%)stretchyGFL/%*symmetricGFL/%(largeopGFL/%.movablelimi tsGFL/%'accentGFL/%'lspaceGQ&0.0emF'/%'rspaceGFen-F,6%Q\"xF'F/F7-FG6-Q \"+F'FDFJFMFOFQFSFUFW/FZQ,0.2222222emF'/FgnF_o-F#6%F@FF-F,6%Q\"yF'F/F7 F+-FG6-Q\"=F'FDFJFMFOFQFSFUFW/FZQ,0.2777778emF'/FgnFjo-FA6$Q\"1F'FDF+" }{TEXT 211 52 " which is impossible, so the system is inconsistent." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 207 9 "Example 2" }{TEXT 211 179 ". He re is another matrix representing the coefficients of a linear system. Write the system corresponding to it and solve the system correspondi ng to the augmented matrix ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "A1:=<<3,1>|<1,5>|<-1,1>>;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "b1:=<1,3>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ReducedRowEchelonForm();" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 9 "Example 3" }{TEXT 211 143 ". This example is showing another w ay of definig matrices in Maple. However, this format is not appropria te for defininig the augmented matrix." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "A2:=Matrix([[2,1,0,3],[-1,0,2,4],[4,-2,7,0]]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "b2:=Matrix([[1],[2],[1]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ReducedRowEchelonForm(A2) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 52 "Same matrix as above define d as in Examples 1 and 2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "A3:=<<2,-1,4>|<1,0,-2>|<0,2,7>|<3,4,0>>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "b3:=<<1,2,1>>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ReducedRowEchelonForm();" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 209 9 "Example 4" }{TEXT 211 92 ". Let us look at an exerc ise 8(d) section 1.2 (Anton&Rorres). We define te matrix as before:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "A4:=<<0,1,3,-2,1>|<10,4,2, -8,-6>|<-4,-1,1,2,3>|<1,1,2,-2,0>>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "b4:=<1,2,5,-4,1>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ReducedRowEchelonForm();" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 211 15 "If we want the " }{TEXT 210 8 "solution" }{TEXT 211 53 " to the above system we need to call a Maple package:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "linsolve(A4,b4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }