Re: what is my error?

*To*: mathgroup at smc.vnet.net*Subject*: [mg100465] Re: [mg100438] what is my error?*From*: "David Park" <djmpark at comcast.net>*Date*: Fri, 5 Jun 2009 03:00:03 -0400 (EDT)*References*: <18096534.1244101248730.JavaMail.root@n11>

Richard, eqns = {mr + mp == 13, fr + fp == 19, mr + fr == 15, mp + fp == 17}; These equations are not all independent so if we use NSolve or Solve or Reduce we do not obtain a complete solution. Reduce[eqns] mp == 13 - mr && fr == 15 - mr && fp == 4 + mr We can see this by setting up the matrix and rhs to use LinearSolve: m = ( { {1, 1, 0, 0}, {0, 0, 1, 1}, {1, 0, 1, 0}, {0, 1, 0, 1} } ); b = {13, 19, 15, 17}; Det[m] 0 But, LinearSolve will obtain a solution as long as the rhs is linearly dependent in the same way as the rows of the matrix are. lsols0 = LinearSolve[mat, {13, 19, 15, 17}] lsols1 = {mr, mp, fr, fp} -> lsols0 // Thread {-4, 17, 19, 0} {mr -> -4, mp -> 17, fr -> 19, fp -> 0} eqns /. lsols1 {True, True, True, True} David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Richard Palmer [mailto:rhpalmer at gmail.com] eqns = {mr + mp == 13, fr + fp == 19, mr + fr == 15, mp + fp == 17}NSolve[eqns, {mr, mp, fr, fp}] gives {{mr->-4.+1. fp,mp->17.-1. fp,fr->19.-1. fp}} The solution is {mr->8, mp->5, fr->7, fp->12} if mr,mp,fr,fp are greater than zero -- Richard Palmer