Results 1 to 2 of 2
Like Tree2Thanks
  • 2 Post By Deveno

Math Help - null space

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    608

    null space

    I have attached the question. Am not sure how to work this, out expect by guessing?


    2 0
    0 3 multiply that by 3,-2 = 0 ,


    is this correct ? or is there 'proper way of working this out ?
    Attached Thumbnails Attached Thumbnails null space-screen-shot-2014-06-10-10.46.40.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,397
    Thanks
    760

    Re: null space

    We want:

    $\begin{bmatrix}a&b\\c&d \end{bmatrix} \begin{bmatrix}3\\-2 \end{bmatrix} = \begin{bmatrix}0\\0 \end{bmatrix}$

    but also:

    since the null space is spanned by a single vector, nullity(A) = 1.

    Now, nullity(A) + rank(A) = 2, therefore: rank(A) = 1.

    So let's make A into a rank 1 matrix the easiest way possible, by setting c = d = 0.

    This gives us the single equation:

    3a - 2b = 0.

    If we pick any value we like for b, a is completely determined as a = 2b/3.

    To avoid fractional values, let's pick b = 3. What matrix do we get?

    By the way, there is more than one correct way to do this, there are MANY possible matrices that would work.
    Thanks from Tweety and HallsofIvy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question on null space/column space/row space of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 1st 2011, 01:47 PM
  2. Replies: 1
    Last Post: January 14th 2011, 09:51 AM
  3. [SOLVED] range space and null space
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 28th 2010, 05:02 AM
  4. [SOLVED] range space and null space
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 23rd 2010, 07:05 AM
  5. column space, null space
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: August 31st 2008, 09:49 AM

Search Tags


/mathhelpforum @mathhelpforum