List Archives >  Maple User Group List Archive >  Archive by date >  This Month By Date >  This Month By Topic

[MUG] solving linear equation

Search email archive for  

[MUG] solving linear equation
Author: Alain Goupil    Posted: 19/10/2000 17:34:45 GDT
>> From: Alain Goupil "goupil" Dear maple users, Here is a problem : The following maple command for solving the linear equation 2x+3y=ax+by for a and b does not return the expected answer : > solve({2*x+3*y=a*x+b*y},{a,b}); {a = (2*x+3*y-b*y)/x, b = b} Is there a way to obtain the answer a=2, b=3 straightforwardly with the solve command ? I know that I could use matrices or the coeff command but I want to stay elementary. Thank you, Alain Goupil

[MUG] Re: solving linear equation
Author: Maple Group    Posted: 23/10/2000 13:56:28 GDT
>> From: Maple Group "maple_gr" | >> From: Alain Goupil "goupil" | The following maple command for solving the linear equation | 2x+3y=ax+by for a and b does not return the expected answer : | | > solve({2*x+3*y=a*x+b*y},{a,b}); | {a = (2*x+3*y-b*y)/x, b = b} | | Is there a way to obtain the answer a=2, b=3 straightforwardly with | the solve command ? I know that I could use matrices or the coeff | command but I want to stay elementary. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 20 Oct 2000 16:10:17 -0500 From: Robert J Lopez "r.lopez" Subject: solving linear equation To: "maple-list" Use the solve/identity command. solve(identity(2*x+3*y=a*x+b*y,x),{a,b}); RJL -- Robert J. Lopez Department of Mathematics Rose-Hulman Institute of Technology Terre Haute, IN 47803 812 877-8396 (office) 812 877-8883 (Department fax) "r.lopez" -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 20 Oct 2000 17:27:32 -0400 From: "David L. Johnson" "david.johnson" To: "maple-list" Subject: solving linear equation Well, I don't know if this is what you mean, but: solve({subs({x=1,y=0},2*x+3*y=a*x+b*y),subs({x=0,y=1},2*x+3*y=a*x+b*y)},{a,b}); works You have to convince Maple that the numbers a and b play a different role than x. As far as it's concerned they are all variables. To solve for the two variables {a,b} you need two equations. Using coeff will do that, but so does this, clearly. -- David L. Johnson "david.johnson" Department of Mathematics http://www.lehigh.edu/~dlj0/dlj0.html Lehigh University 14 E. Packer Avenue (610) 758-3759 Bethlehem, PA 18015-3174 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Nathan Sokalski" "njsokalski" To: "maple-list" Subject: solving linear equation Date: Sat, 21 Oct 2000 00:35:40 EDT The reason you do not recieve a=2, b=3 is because that is not the only correct solution. if you go through the following process, you can see where Maple gets its answer: 2x+3y=ax+by 2x+3y-by=ax (2x+3y-by)/x=a You can also see by looking at these simple Maple statements that this is always true: STUDENT>restart; STUDENT>a:=(2*x+3*y-b*y)/x; 2x+3y-by a:= ---------- x STUDENT>testeq(a*x+b*y=2*x+3*y); true STUDENT>b:=37;a; b:=37 2x-34y a:=-------- x STUDENT>a*x+b*y; 2x+3y If you enter these commands into Maple, notice that you can change the value of b (it is 37 in the example) to any value you want, but you will always recieve 2x+3y when entering a*x+b*y Nathan Sokalski "njsokalski" -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "wh.werner" (wh.werner) To: "maple-list" Subject: solving linear equation Date: Sat, 21 Oct 2000 10:11:56 +0200 Hallo. I guess you implicitly assumed that your equation 2*x+3*y=a*x+b*y is valid for any value of x and y. You did'nt pass this information to Maple however! So don't expect that Maple can return another answer than it does. If you use the "coeff" command however this implies all information concerning the expected solution. Regards Wilhelm Werner -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: Gaston Gonnet "gonnet" Date: Sat, 21 Oct 2000 19:00:08 +0200 (MET DST) To: "maple-list" Subject: solving linear equation In this case you can use "identity", e.g. > solve( identity( 2*x+3*y=a*x+b*y, x), {a,b} ); {a = 2, b = 3} (This works for only one variable, in the case above it was enough) See ?solve,identity for more details. Gaston Gonnet -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Daniel Frenkel" "jfrenkel" To: "maple-list" Subject: solving linear equation Date: Sat, 21 Oct 2000 21:30:53 -0200 Dear Alain, Try using "match" command: > match(2*x+3*y=a*x+b*y,{x,y},'s'); true > s; {b = 3, a = 2} Cheers, Daniel Frenkel "frenkel" -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 23 Oct 2000 10:29:05 +0200 (CEST) From: "elbr" To: "maple-list" Subject: solving linear equation You have to use a variant of solve (see solve,identity):: 2*x+3*y=a*x+b*y; solve(identity(%,x),{a,b}); 2 x + 3 y = a x + b y {b = 3, a = 2} E. Elbraechter ---------------------------------- E-Mail: "elbr" Date: 23-Oct-2000 Time: 10:22:25 ---------------------------------- -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Mon, 23 Oct 2000 12:35:06 +0100 From: Barsuhn "barsuhn" Subject: solving linear equation To: "maple-list" Dear Alain, your equation has infinitely many solutions, among these is a=2, b=3. If you insert b=3 into the formula you found for a, you get a=2. I suppose you wish to do something quite different. You see that your expression 2x+3y is of the type ax+by and would like to see which values for a and b will lead to an exact match. This is done by the following statements. The first statement finds that the attempt to match succeeds. The equations that yield the exact match are assigned to the variable substitution: > match(2*x+3*y=a*x+b*y,{x,y},'substitution'); true > substitution; All the best Jurgen {b = 3, a = 2} -- ------------------- Prof. Dr. Jurgen Barsuhn Fachhochschule Bielefeld University of Applied Sciences Fachbereich Elektrotechnik und Informationstechnik Wilhelm-Bertelsmann-Str. 10 D-33602 Bielefeld -----------

[MUG] Re: solving linear equation
Author: Maple Group    Posted: 31/10/2000 01:12:22 GMT
>> From: Maple Group "maple_gr" Alain Goupil wrote: | The following maple command for solving the linear equation | 2x+3y=ax+by for a and b does not return the expected answer : | | > solve({2*x+3*y=a*x+b*y},{a,b}); | {a = (2*x+3*y-b*y)/x, b = b} | | Is there a way to obtain the answer a=2, b=3 straightforwardly with | the solve command ? I know that I could use matrices or the coeff | command but I want to stay elementary. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 24 Oct 2000 11:22:23 +0100 From: "Dr Francis J. Wright" "F.J.Wright" To: "goupil" Subject: solving linear equation You only expect the answer a=2, b=3 because you know that x and y are variables (rather than constants) and that they are independent; otherwise, your expectation would not be correct. So you need to provide Maple with this additional information. As you remark, this could be done using coeff. Another way is to use partial differentiation to express the independence of x and y, as follows, where the final solve is almost superfluous: > 2*x+3*y=a*x+b*y; 2 x + 3 y = a x + b y > map2(diff, %, {x,y}); {2 = a, 3 = b} > solve(%, {a,b}); {a = 2, b = 3} Francis -- Dr Francis J. Wright | mailto: "F.J.Wright" School of Mathematical Sciences | tel: (020) 7882 5453 (direct) Queen Mary, University of London | fax: (020) 8981 9587 (dept.) Mile End Road, London E1 4NS, UK | http://centaur.maths.qmw.ac.uk/ -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Wed, 25 Oct 2000 09:07:28 -0500 From: Herman Jaramillo "herman.jaramillo" To: "maple-list" Subject: solving linear equation You have one linear equation with two unknowns. The solution is a stright line. (2,3) happens to be one point of that line, but Maple is giving you all solutions (one degree of freedom "b") -- Herman Jaramillo phone: 713-689-6503 Research Geophysicist fax : 713-689-6100 Baker Hughes (Western Geophysical) email: "herman.jaramillo" 3600 Briarpark Drive (77042-5275) P.O. Box 2469 Houston, Texas 77252-2469 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: "Willard, Daniel Dr DUSA-OR" "Daniel.Willard" To: "''" "maple-list" Subject: solving linear equation Date: Mon, 23 Oct 2000 10:26:28 -0400 I am afraid you are uninformed about solving linear, or perhaps non-linear too, equations. To solve for two variables (a and b) you need two equations. Consider a graph in which a and b are plotted on perpendicular axes. Assuming that you know x and y, the plot of ax + by is a line, not a point. You need a second line intersecting it at that point to have such a solution. Maple cannot do the impossible; it has done what it can with your statement of the problem.

Previous by date: [MUG] Re: printing plots with G-4, Bauldrywc
Next by date: [MUG] Step-by-step solving and verifying of differential equations, Chuck Baker
Previous thread: [MUG] table -> plot3d in Maple V R 4, Franck Courchamp
Next thread: [MUG] Step-by-step solving and verifying of differential equations, Chuck Baker