Results 1 to 3 of 3

Math Help - Eigenvector

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    7

    Eigenvector

    In the attached example, how to reduce to -v1+2v(subscript 2)=0 ? Thank you

    Eigenvector-q1.jpg
    Last edited by jasonmark; August 5th 2008 at 11:06 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by jasonmark View Post
    In the attached example, can do I reduce to the equation -v1+2v2=0 ? Thank you

    Click image for larger version. 

Name:	q1.jpg 
Views:	14 
Size:	29.1 KB 
ID:	7420
    To get from here

    \bigg[\begin{array}{cc}2&2\\-1&5\end{array}\bigg]\bigg[\begin{array}{c}v_1\\v_2\end{array}\bigg]=\bigg[\begin{array}{c}3v_1\\3v_2\end{array}\bigg]

    to here

    -v_1+2v_2=0

    We do this:

    First multiply the matrices together:

    \bigg[\begin{array}{cc}2&2\\-1&5\end{array}\bigg]\bigg[\begin{array}{c}v_1\\v_2\end{array}\bigg]=\bigg[\begin{array}{c}3v_1\\3v_2\end{array}\bigg]=\bigg[\begin{array}{cc}2v_1&2v_2\\-1v_1&5v_2\end{array}\bigg]

    Now set the two matrices equal to each other:

    \bigg[\begin{array}{cc}2v_1&2v_2\\-1v_1&5v_2\end{array}\bigg]=\bigg[\begin{array}{c}3v_1\\3v_2\end{array}\bigg]

    We can write the matrices as a system of equations:

    \left\{\begin{array}{rcl} 2v_1+2v_2 & = & 3v_1\\-v_1+5v_2 & = & 3v_2\end{array}\right.

    Thus, if we set each equation equal to zero, we have

    \left\{\begin{array}{rcl} -v_1+2v_2 & = & 0\\-v_1+2v_2 & = & 0\end{array}\right.

    Now, how do we determine v_1 and v_2?

    There are infinitely many solutions.

    I'll pick a simple one: v_1=1 and v_2=\tfrac{1}{2}

    These two values, and any integer multiple of them will satisfy the equation we came up with.

    Does this make sense?

    --Chris
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    7
    Thanks a lots!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: April 11th 2011, 01:18 PM
  2. eigenvector
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: January 22nd 2011, 10:39 AM
  3. Eigenvector
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 9th 2010, 04:43 AM
  4. eigenvector
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 21st 2010, 03:24 PM
  5. eigenvector of A+I
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 9th 2009, 04:17 PM

Search Tags


/mathhelpforum @mathhelpforum