Notices
Results 1 to 4 of 4

Thread: linear equations

  1. #1 linear equations 
    Forum Freshman E(i)lusiveReality's Avatar
    Join Date
    Jan 2011
    Location
    Meerut,India
    Posts
    17
    why cant a set of two linear equations in two unkowns have exactly two solutions.While it is easy to see geometrically. How can we prove it algebrically ?


    Import > Export. That the favourable Economic Ratio for the human mind .
    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Ph.D. Heinsbergrelatz's Avatar
    Join Date
    Aug 2009
    Location
    Singapore
    Posts
    994
    using simultaneous equation..


    ------------------




    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


    -------------------
    Reply With Quote  
     

  4. #3 Re: linear equations 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by E(i)lusiveReality
    why cant a set of two linear equations in two unkowns have exactly two solutions.While it is easy to see geometrically. How can we prove it algebrically ?
    If the equations are homogeneous, the solutions form a vector space. The only finite vector space is the zero vector space.

    If the equations are not homogeneous, a general solution is any single solution plus solutions of the associated homogeneous equations. Thus there is either no solution, a unique solution or infinitely many solutions.

    This also applies to n equations and m unknowns.
    Reply With Quote  
     

  5. #4  
    Forum Ph.D.
    Join Date
    Jul 2008
    Location
    New York State
    Posts
    857
    If you think about it geometrically, it is easy to understand. Each equation is a line in the plane and the solution is the (x,y) coordinate where the lines cross. If they are parallel, there is no solution.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •