
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 3rd, 2014, 09:29 AM  #1 
Newbie Joined: Nov 2014 From: turkey Posts: 9 Thanks: 0  Systems of Linear Equations(Immediate)
Suppose that a system of linear equation in four variables has ten equations. Does it mean that the solution set cannot have free variables? 
November 3rd, 2014, 09:36 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2642 Math Focus: Mainly analysis and algebra 
It depends. If the equations are inconsistent, there are zero solutions. If the equations are consistent and there is a set of four of them that are linearly independant, there will be a unique solution with no free variables. If the equations are consistent and there is a set of three of them that are linearly independant (but no such set of four), there will be a solution having one free variable. If the equations are consistent and there is a set of two of them that are linearly independant (but no such set of three or four), there will be a solution with two free variables. If the equations are consistent but none are linearly independant (i.e. all the equations are equivalent), there will be a solution having three free variables. 

Tags 
equationsimmediate, linear, systems 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Systems of 3 Linear Equations solutions  Sadia  Linear Algebra  6  September 27th, 2014 05:18 PM 
Systems of Linear Equations  kaspis245  Algebra  9  August 8th, 2014 10:07 AM 
Proof about linear systems of equations  david940  Linear Algebra  2  July 25th, 2014 06:12 PM 
Nonlinear systems of equations  Akcope  Calculus  3  March 14th, 2014 01:49 AM 
Help on Systems of linear equations  Jake_88  Linear Algebra  1  June 15th, 2010 05:59 AM 