0002000201000bSystems.ACT00050200171_NonlinearSystem 1.EAC010000002b16É 1_NonlinearSystem 1.EAC†Œs.ACT†*†-†7ˆ:†>Š †F†QkE Ž'[†)Œ`s†ŠOŽ’€ ŽŽ0Solve by Substitution–>†¿ [†sŒ^x+yŒj2Œr=8Œxy=Žx,y\Œ‘GraphÌˆ`†dÊŒ÷SGraph2DT† †Š3Šh†ˆLISTSYSˆt4N†Modify†;¨†($ˆ<STATCALCÌ†Uˆ(ˆŒ<Ô\ˆ<Sequence0†<,ˆxShee†]†Œ\†|’ŠŒØ’olveEq†´ˆ´LwrX†Í(Upˆd’tupFLG1p†<(Š<†Lis†Ø˜†dD‰ˆPic†ìÜÜViewWin†L‡0‰,x2Š±†‡EH†y†^Ž8†ˆä’P äŠGŠˆðŠ´ä’‹|ˆÈä’‡|ŒÜäŽx €†ä† † Œ’’˜’’¤’’°’’¼’’È’’Ô’’à’’ì’’ø’È’ Ü’!ðˆnŒ"‘(’#‘4’$‘,@’%‘@L’&‘TX’'‘hd’ˆn‹p’)‘|’*‘¤ˆ¸†ä+†”† †,’ ’-’¬’.’¸’0’Ä’1’Ð’2’Ü’3’è’4’ô’5´ˆ½ŒEÈ’FÜ’Hð$’I‘ˆ¾ŒJ‘<’K‘,ˆFŒL‘@T’M‘T`’N‘hl’O‘|x’P‘„’Q‘¤’R‹¸œ††äS††¨’T’´’]’À†A ˆ^’Ä’_’È’`’Ì’a’Ð’b’Ô’”’Ø’Œ•’ä’Í’ð’Î’ü’ˆnŠó‘††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~ƒˆÁŽŽž’ ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿxˆÁˆŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŠŽž¾ Â@††a†n seq_histb†NewFoldeŠ…ˆ3 ’ systemä]l†0’^]=” –À††î<ˆxö<þxìðsystemä]list’^]= †,ˆÁŠŒö<þxþ´äð† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5–@heetSˆ3D††† †0†@†PŠ$ 1èê¬^Œ42ž3ž 4ž 5ž ˜|†x Š†‘i™”™††Š †¶ ¸Dkäûxˆ½ŽÀ††$’S’\¢œ“²<‡Žh†(¦dˆË 6y-y^2+8–‡f3x2/xŒOŽ`–P‘¬$P†`”†$””T`–ª< ™`”`”˜0 ˆ–(1…0qy`ˆ„#Y‡uYƒ† ˜–˜œšH®Æ$ÊH—,®ÀšÍ®°´ÎI†Œ˜ °à1ða’®`’¾ ™†QŠÍ[Œ;[Œ Solving the first equation Ž#for x, and substitute it ŒLintoŠ@seco†%A.\Œm CalculatorËˆ†ƒßŒŸ Rˆ í¸í¹=2|x=Ž-yŒ2Œ$+8RŽ&-Œ?yŒGî’”yžA’.8Œu=aŠ‹ŒŠexpand(ans)¤o¢[3Œœ+’“Ž]†‹œœªnrewritežoÊpÂqï@’0–ï ansî(-1¦~¢å-šu î’ˆ yŽ+Ž2Ž=Ž 0RŠ0Š-nveÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[×ÁŽŽž¾ ¤@×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx×Á×ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em×ÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–@”0–, cx”sh† ™wg'''1† `Id666@†ˆ+ˆ/†0’†?(1…0qy`ˆH#Y‡uYƒ†U ˜–0–˜H®Æ$ÊHi9”pV¢´šÁ²’ñ²´úUú’“†Œ˜ °˜’® `t($OŠ"[Š< We have yŒ3Ž-8î’y+2=0.[Œ-Ž Using CAS,\ŽGCalculatorËˆ,†0ßŠ† Rˆsolve(ŽyŒ3Œ$-”8Œ7î’-ŒH+ŒP2ŒX=Œ`0,y)Ršc&Ž‡-Œ?2.94599520I,¦6Œ\0.2†)00385–.¬-†Z 693994817‹‰ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[×ÁŽŽž¾ ¤@×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx×Á×ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em×ÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Š; The result isŽ y=-2.945995202ŽŠ 0.2†00385ž2.693994817 Žb[Œk Substitute t”vto Œ‹ˆfirst equation.\Œ¦ CalculatorËˆV†Zß;¤ R†x =Ž-yŽ2Ž&+8|y’1Ž-Œ.2.945995202RQx®20.67888773ˆ3ê–œ• =0.2†00385°†Œú7.936495806ÿ“T 2.693994817¯ 0.74239192Š„‡—‡œ‡ŸÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ˆÁŽŽž¾ ¤@ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿxˆÁˆŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emˆÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Š;The final result are[Œ#xŒ+y=˜ -0.6788877302Œ -2.945995202ÚN7.936495806Œ¢0.2†G00385ÞL 0.74239192ŽL2.693994817‰ ‰E Try your own.\GraphÐˆ*†.Ê®ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ˆÁŽŽž¾ ¤@ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿxˆÁˆŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emˆÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq\Š; CalculatorËˆ)†ßŽ•RˆQŒ.Œ«ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[×ÁŽŽž¾ ¤@×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx×Á×ŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸×ÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ em×ÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eAct0200172_NonlinearSystem 2.EAC010000000eefÉ 2_NonlinearSystem 2.EAC†Œs.ACT†*†-†7ˆ:†>Š †F†QkE Ž'[†)Œ`s†ŠOŽ’€ ŒŽ/Solve Numerically–9†º [†nŒX y-log(x)+1=0Œkxy=2Œx,y\ŒGraphÌˆU†YÊŒçSGraph2DT† †Š3Šh†ˆLISTSYSˆt4N†Modify†;¨†($ˆ<STATCALCÌ†Uˆ(ˆŒ<Ô\ˆ<Sequence0†<,ˆxShee†]†Œ\†|’ŠŒØ’olveEq†´ˆ´LwrX†Í(Upˆd’tupFLG1p†<(Š<†Lis†Ø˜†dD‰ˆPic†ìÜÜViewWin†L‡0‰,y†JŠ³‡EHˆ2’8†ˆä’P äŠGŠˆðŠ´ä’‹|ˆÈä’‡|ŒÜäŽx €†ä† † Œ’’˜’’¤’’°’’¼’’È’’Ô’’à’’ì’’ø’È’ Ü’!ðˆnŒ"‘(’#‘4’$‘,@’%‘@L’&‘TX’'‘hd’ˆn‹p’)‘|’*‘¤ˆ¸†ä+†”† †,’ ’-’¬’.’¸’0’Ä’1’Ð’2’Ü’3’è’4’ô’5´ˆ½ŒEÈ’FÜ’Hð$’I‘ˆ¾ŒJ‘<’K‘,ˆFŒL‘@T’M‘T`’N‘hl’O‘|x’P‘„’Q‘¤’R‹¸œ††äS††¨’T’´’]’À†A ˆ^’Ä’_’È’`’Ì’a’Ð’b’Ô’”’Ø’Œ•’ä’Í’ð’Î’ü’ˆnŠó‘††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~ƒˆÁŽŽž’ ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿxˆÁˆŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŠŽž¾ Â@††a†n seq_histb†NewFoldeŠ…ˆ3 ’ systemä]l†0’^]=” –À††î<ˆxö<þxìðsystemä]list’^]= †,ˆÁŠŒö<þxþ´äð† ††††’’,† †0†@†@ PSheet1ˆL€ ´Š2ž3ž 4ž 5–@heetSˆ3D††† †0†@†PŠ$ 1èê¬^Œ42ž3ž 4ž 5ž ˜|†x Š†‘i™”™††Š †¶ ¸Dkäûxˆ½ŽÀ††$’S’\¢œ“²<‡Žh†(¦d ‡W 3xà`(x)-‡;‡fˆ†2/xŒOŽ`–P‘¬$P†`”†$””)A†H‚† `ˆ™‚–qŠ$˜<q•c('†e ™ah@—‡SŠ`ES iŠ`˜0 ˆ–(1…0qy`ˆ„#Y‡uYƒ† ˜–˜œšH®Æ$ÌH9 “u1…‹8Cf„„d ŠäšÁšÎ¬°´ÎH†Œ˜ °à1ða’® `P49X†Ä ˜†QŠÍ[Œ;[Œ Open the graph window, Ž and tap Œanalysis\G-Solve\Intersect. ZGŠQapplication showsŽKˆtresult numer†%lly.[ŽŸxŒ°yŽ°=˜13.92093753185ŒÜ0.143668484642[†ˆ Try your own.\ŒGraphÐˆ*†.ÊŠ4ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ˆÁŽŽž¾ ¤@ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿxˆÁˆŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ˆÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emˆÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eActx ™™”P0200163_Row Echelon Form.EAC010000001745É 3_Row Echelon Form.EAC†Systems.ACT†)†,†6ˆ9†=Š †E†PkE Ž'[†)ŽP†ŠOŽ Ž –>†¾ [ˆŸŒ] x-2y+z=7Œl 3x-5ˆ14Œ} 2ˆ!-z=3Œ0x,y,z’šŽFThe augmented matrix is, ˆmŒÊ1ŒÒ-2œŽŽf-5ž2Ž:’C-ŽU<.–Reduce the row to R† Echelon Form.\Œ CalculatorËˆ'†+ßˆ1$Rˆ1Œ-2œ7Ž3!5ž214ŽŽ:’C-ŽU3RžpŽ6-œ>¤x )´€¢S d–†ŒúmRowAdd(-3,ans,1,2)ö¯0²à ñáè·*mRowAdd(-2,ans,1,3)R1Ž -Ž2Ž7Ž0²1 B 2¢!3žt11RˆŒ“ ¸2þ¸²é ú ê’ò+3–¥‰<¨N(°FinaForm¸$N†Graph2D†Ü†& 3ŠðˆLISTSYSˆü†@4ˆ<Modify 0ˆPˆ<STATCALC TˆdˆŒ< \\ˆxSequenceˆŒ,ˆxSheetˆOä|’ŠŒ`’o lveEqˆˆ´†~`wràˆ´(Upˆì’tupFLG1ø(Š<†Lis†{ D‰ˆPic†dÜViewWin†ˆˆŒ_osve†v‡4¤xä‰‰°Œä’¼ ä’È´ä’ÔÈäŽP à‰ †ä† † ‡^†— ’ø’†¬!’<’P’d(’†u4’ˆ2Š@’†rL’†rX’†rd’ Üp’!ð|† "‘ˆ† #‘”† $‘, † %‘@¬† &‘T¸† '‘hÄ’‰‹Ð†)‘Ü† 0*‘¤è¸†ä+†ô† †,ˆŒ-(†„.<† 0P$† 1d†%†%2x<†3ŒH† 4 T† 5´`† EÈl† F†Öx’ˆZŠó„†ŽI†Ö† J†Öœ† K†Ö¨† L†Ö´† M†ÖÀ† N†ÖÌ† O‘|Ø† P†Öä† Q†Öð‡0R‹¸†Öü††Ñ†å S††‡Oˆ˜†]‡[ †A ˆ^†ˆÖ_†(†ˆ´,†a†0†b†4†‰u8’Œ•†D†Í†P†Î†\†‰hh†×‡¸t’Ø†€†Ù†Œ†Ú†˜†Û†K¤‘h Financial‡‚Forma†n †ˆ† †ˆŒE‡¥” systemä]listˆŠ^]=’_Œ†`Šaˆ" b~QÁŽŽž¾ þ@þ€þÀÿÏ@ÁŒQ ÿ@ÿx‡¸°:ŒŽXŠ”XÖ¸Œ»†a†ö seq_h†b†NewFolde‹ ˆ3 ’ ˆÔ’Ó†0’ŠÎ ” —H††‡î<ˆxÒ<ŒÄˆˆ†š<‡’“ ö<ö<þxþðÿ,ÿh†<N†‰†Œ †ˆo† †0†!@†0PSheet1úê¬^Š2ž3ž 4†5ž ŒH3DÊ|èš|š†††ŠK˜| “i™”™††Š ˆŽ‰FkE ‰9ŽÀ‰`†$«d«yŽ “€« ‰µ†I††††ŠŽ †`–P2Æ$´$’y–p”x”–<” ™€–`’œ0˜ä(1…0qy`ˆä#Y‡uYƒˆH˜–˜œšHª„Æ$ÎH™Œ™˜žˆË†Œ˜ ’ˆQ–Â9ÂZÂ{ÂœÂ½¶Þ˜Ø¬ð†ˆü†c€‘+`”–œ™YVˆ¸[ŒŒ We have Œ1Œ'-2œ7Œ@0¤) -7Š 0ŽŽ1Ž3Ž .[Œ*This matrix shows, Ž x-2y+z=ŽYy-2z=gz=ŽQx,y,zUSubstitute z to the Œšsecond equation.RŠ¹Š] †]î3†_RŽy-6Š’'ans+6–#y=-1|š|a†kyœ‚firstª †í î(-1)+3=˜…x+5ˆš„-5–"x=2‘TThenŠôsoluˆæ i‡W—Xx’y²z=2Œ-1Ž3[Œ(\Œ0Hint to use CAS.Ëˆ †$ßˆRRŠ^Œeref(ŠiŽiŽ`-Žr7Ž3!5ž214 ¬¤µŽÜ)Rœxê-œò¢€0²1 B 2’:Ž†3‹o!ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Œ;†ˆD Try your own.\Œ CalculatorËˆ/†3ßŠˆµRˆnŽKŠÉÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eAct02000a4_RREF.EAC0100000016c4É 4_RREF.EAC†Systems.ACT†† †*ˆ-†1Š †9†DkE Ž'[†)ŽP†Š5[ŒReduced Row Echelon Form Œ)<ˆ•>’7Œ [ˆ˜ŒV x-2y+z=7Œe 3x-5ˆ14Œv 2ˆ!-z=3Œ0x,y,z˜“‡The augmented matrix is, ˆmŒÃ1ŒË-2œŽŽf-5ž2Ž:’C-ŽU<. ! the r‡$to ‹§\I CalculatorË†ß†† üRˆ1Œ-2œ7Ž3!5ž214ŽŽ:’C-ŽU3RžpŽ6-œ>¤x )´€¢S d–†ŒúmRowAdd(-3,ans,1,2)ö¯0²à ñáè·*mRowAdd(-2,ans,1,3)R1Ž -Ž2Ž7Ž0²1 B 2¢!3žt11RˆŒ“ ¸2þ¸²é ú ê’ò+3–¥‘]¤1©\Žj0¡d¡©e-Œ2Ž 7Ž0ŽŽ1Ž13Rˆ@Œ>mRowAdd(3,ans,3,1)Rž9 Q2ži1 Šþ›Ž›2Ž›2ø›Ž’0¡-°Ü©-‰wÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Œ;[Œ We have Œ 1Œ(0ŽŽ2žž(-°93Œ&$. This matrix shows the solution is,Œ”ŽªxŒ¼yŒÄzŒÌ=œ'Ž£”‹Žs.ý\Hint to use CAS.Ëˆ †$ß Rˆ rref(Œ1Œ-2œ7Œ43!5ž214ŒVŽ:’C-ŽU<)R¨x0ŽŽM’’(ŽÄ-¾A’|ŠúŒù‰ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Œ;†ˆD Try your own.\Œ CalculatorËˆ/†3ßŠˆµRˆnŽKŠÉÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eAct02000f5_RREF_MORE.EAC01000000120cÉ 5_RREF_MORE.EAC†Systems.ACT†"†%†/ˆ2†6Š †>†IkE Ž'[†)ŽP†Š5[ŒReduced Row Echelon ŽForm Œ1<ˆ¢>’?ŒV[ˆ¥Œc -í¸+2í¹=2Œs††4Œ2Œ6Œí¸,í¹ˆ•‡When solve the s‹ŽŠof equaˆrs using rref:R‹Œàˆ(ˆŒ-1Œ{Ž‘Ž Ž£¢ Ž¬)R‰}\1Š0Ž2ž 00[ŒBThe result indicates that Œcour solution is:[Ž@xŽŠyŽQ=š™2\Œ²GraphÎˆ¿†ËÎˆÑŽˆˆÚ™™™™™™†`ŠˆˆŒ—††…Š•ŠŽD‰vŽ.ˆ`r† ŽmA† 'LŽ'‰JC˜ u˜x˜yŽ †qˆqˆ¹Ä@ ¤ˆÂH!ŠA@‡±Ð6–°†2†ŒŠ’Œ†'ÊÀ! Š@†6Ð6–°†=G!5•I™†H Y™”Bq™˜† –Yˆ†iÄ@ T††ÉÀ ¦XgfŠL–™‚„'GF†.`FŠFÈ¨F˜’”ª ™h2W)ˆ™ŠFˆˆˆäŽíˆˆWˆ_‰#ˆ,[‰#ŽŒ‰4 [†LŒ+ í¸+3í¹=2Œ:-††4ŒI2Œ6Œ-í¸,í¹[Ž;When solve the system Œƒ of equations using rref:Rˆˆ(Œ1Œ3Œ#2Œ+-!4œ!’6Œ\)Rª\0ŽŽ’¾ 1[Ž¹The third row †ìˆÊ Ž× indicates†$ at 0í¸+0í¹=1 Œ÷has no solu‰ .\GraphÎ‰ ‡'Î‰-†‰6ˆˆ`ˆ†`WP‡VspŽD‰svŽŠQr† A† 'L††C˜ u˜x˜yŽ †<† †E‰J Š@†TÐ6–°†[”Bq™˜†f ™G!5•I™Šh2W)ˆ`ˆ3†‡ˆ@¨Bgf†6Y™” ™‚„'GFB´B"wfiŠ„ Hh2˜Š2EU28ŠZˆ4ˆËˆGˆˆÓ‰ˆ$[‰%Š‰. Try your own.\Œ CalculatorËˆ/ †3ß‹*‰iR‰IŽK‹}ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq\Š;GraphÌˆ$†ÊŒÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ÂŽŽž¾ ¤@ÂŽŽž¾ þ@þ€þÀÿÿ@ÿxÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ÂŠŽž° ††a†F seq_histb†RFlashBooŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emÂŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úúd_Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èúd_Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eAct010008main.ACT0001020012eActivity Save.EAC01000000120cÉ 5_RREF_MORE.EAC†Systems.ACT†"†%†/ˆ2†6Š †>†IkE Ž'[†)ŽP†Š5[ŒReduced Row Echelon ŽForm Œ1<ˆ¢>’?ŒV[ˆ¥Œc -í¸+2í¹=2Œs††4Œ2Œ6Œí¸,í¹ˆ•‡When solve the s‹ŽŠof equaˆrs using rref:R‹Œàˆ(ˆŒ-1Œ{Ž‘Ž Ž£¢ Ž¬)R‰}\1Š0Ž2ž 00[ŒBThe result indicates that Œcour solution is:[Ž@xŽŠyŽQ=š™2\Œ²GraphÎˆ¿†ËÎˆÑŽˆˆÚ™™™™™™†`ŠˆˆŒ—††…Š•ŠŽD‰vŽ.ˆ`r† ŽmA† 'LŽ'‰JC˜ u˜x˜yŽ †qˆqˆ¹Ä@ ¤ˆÂH!ŠA@‡±Ð6–°†2†ŒŠ’Œ†'ÊÀ! Š@†6Ð6–°†=G!5•I™†H Y™”Bq™˜† –Yˆ†iÄ@ T††ÉÀ ¦XgfŠL–™‚„'GF†.`FŠFÈ¨F˜’”ª ™h2W)ˆ™ŠFˆˆˆäŽíˆˆWˆ_‰#ˆ,[‰#ŽŒ‰4 [†LŒ+ í¸+3í¹=2Œ:-††4ŒI2Œ6Œ-í¸,í¹[Ž;When solve the system Œƒ of equations using rref:Rˆˆ(Œ1Œ3Œ#2Œ+-!4œ!’6Œ\)Rª\0ŽŽ’¾ 1[Ž¹The third row †ìˆÊ Ž× indicates†$ at 0í¸+0í¹=1 Œ÷has no solu‰ .\GraphÎ‰ ‡'Î‰-†‰6ˆˆ`ˆ†`WP‡VspŽD‰svŽŠQr† A† 'L††C˜ u˜x˜yŽ †<† †E‰J Š@†TÐ6–°†[”Bq™˜†f ™G!5•I™Šh2W)ˆ`ˆ3†‡ˆ@¨Bgf†6Y™” ™‚„'GFB´B"wfiŠ„ Hh2˜Š2EU28ŠZˆ4ˆËˆGˆˆÓ‰ˆ$[‰%Š‰. Try your own.\Œ CalculatorËˆ/ †3ß‹*‰iR‰IŽK‹}ÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[QÁŽŽž¾ ¤@QÁŽŽž¾ þ@þ€þÀÿÿ@ÿxQÁQŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸QÁŠŽž° ††a†F seq_histb†NewFoldeŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emQÁŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úê¬^Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èê¬^Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq\Š;GraphÌˆ$†ÊŒÀSGraph2D,† †Š3Š@†ˆLISTSYSˆL4N†Modify†;€†($ˆ<STATCALC¤†Uˆ(ˆŒ<¬\ˆ<Sequence†<,ˆxSheet†Š4†|’ŠŒ°’olveEq†´ˆ´Lwr0†Í(Upˆ<’tupFLG1H†<(Š<†Lis†{p†dD‰ˆPic†´ÜViewWindØ†‰,äŠ±‡@ôxäŠ ŠŒä( ä<´äP$Èäd’ÜäŽx <†ä† † H’’T’’`’’l’’x’’„’’’’œ’’¨’ ’´’!’À’"’Ì’#’Ø’$’ä’%’ð’&’ü’'‘@’(‘T’)‘hˆ¾Œ*‘|,’+‘8’ˆ‹§D¸†ä-†P† †.’\’0’h’1’t’2’€’3’Œ’4’˜’5’¤’E’°’F’¼’H’È’I’Ô’J’à’K’ì’L’ø’M‘,’N‘@’O‘T’‰^‹k(’Q‘|‰ŒR‘@’S‘¤ˆ–ŒT‹¸X††ä]††d† ˆ^’h’_’l’`’p’a’t’b’x’”’|’Œ•’ˆ’Í’ˆ2ŒÎ’ ’Ð’¬Ü††ˆŒ!†” system‰list’‡]=’‡‰’†ü‰’†ø‰’†ô~[ÂŽŽž¾ ¤@ÂŽŽž¾ þ@þ€þÀÿÿ@ÿxÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ÂŽŽž¾ þ@þ€þÀÿÿ@ÿx‡¸ÂŠŽž° ††a†F seq_histb†RFlashBooŠ]ˆ3 ’ systemä]l†0’^]=” –˜††î<ˆxö<þxìðÒ´ emÂŠŒsystˆä]list’^]= ö<þxþ´<† ††††’’,† †0†@†@PSheet1úúd_Š2ž3ž 4ž 5ž ‡›ŠX3D´|PSheet1èúd_Š2ž3ž 4ž 5ž ŒH3D Šˆi™”™††Š ˆŽ¸Dkäûx†††$’S’\¢œ”D²<‡Žh†(žŽ `–PÝÆ$´$“$–p”x”,ˆˆ ™€ `”˜$’.ˆ>(1…0qy`ˆH#Y‡uYƒ†U ˜–0–šH®Æ$ÊHš©š¶´¨5°´þaþ ‰¼†Œ˜ °˜’®`–$ ™†OŠq[Ž;eAct0301d7002000080000000016f1xœíÝlç}Çñ;ŠúA…®i‰iåÄm™DméšnDJJ\TäYräF¶KiÀID[ 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