Results 1 to 2 of 2

Math Help - Showing a solution for system of equations

  1. #1
    Member
    Joined
    Jun 2006
    Posts
    93

    Showing a solution for system of equations

    I'm stuck on how to begin this problem...

    Let (c1, c2) be a solution to the 2x2 system

    A11X1 + A12X2 = 0
    A21X1 + A22X2 = 0

    Show that for any real number alpha (a) the ordered pair (ac1, ac2) is also a solution.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member teuthid's Avatar
    Joined
    Feb 2008
    From
    Bowling Green, OH
    Posts
    49
    Plug in (ac_1,ac_2)...
    <br />
A_{11}(ac_1)+A_{12}(ac_2)
    =a\left[A_{11}(c_1)+A_{12}(c_2)\right]
    =a[0]
    =0

    Therefore, if A_{11}(c_1)+A_{12}(c_2)=0, then (ac_1,ac_2) is also a solution to A_{11}x_1+A_{12}x_2=0.

    then repeat the process of the second equation. This process can be done more quickly if you use matrix notation:

    \vec{c} is a solution to A\vec{x}=\vec{0}
    \rightarrow A\vec{c}=\vec{0}

    so, if we test a\vec{c}...
    A(a\vec{c})=aA\vec{c}=a\vec{0}=\vec{0}

    therefore a\vec{c} is also a solution to A\vec{x}=\vec{0}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 18th 2011, 08:11 PM
  2. Solution for system of diff equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 6th 2011, 08:47 AM
  3. Solution of system of linear equations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 23rd 2009, 04:58 AM
  4. System of equations solution description
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 8th 2009, 05:26 PM
  5. Replies: 1
    Last Post: May 3rd 2007, 04:27 AM

Search Tags


/mathhelpforum @mathhelpforum