User Name Remember Me? Password

 Linear Algebra Linear Algebra Math Forum

 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: 7,690 Thanks: 2669 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. Thanks from xsirmath Tags equationsimmediate, linear, systems Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Sadia Linear Algebra 6 September 27th, 2014 05:18 PM kaspis245 Algebra 9 August 8th, 2014 10:07 AM david940 Linear Algebra 2 July 25th, 2014 06:12 PM Akcope Calculus 3 March 14th, 2014 01:49 AM Jake_88 Linear Algebra 1 June 15th, 2010 05:59 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      