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Thread: null space

  1. #1
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    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  
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  2. #2
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    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
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