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Math Help - Span and Kernel

  1. #1
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    Span and Kernel

    What would be the kernel of a 2x2 identity matrix. I put 0, I'm just making sure this is correct? Also, a 3x3 matrix 0 1 0, 0 0 1, 0 0 0. How would I do the kernel of this when x1 would be undefined?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by cwarga88 View Post
    What would be the kernel of a 2x2 identity matrix. I put 0, I'm just making sure this is correct? Also, a 3x3 matrix 0 1 0, 0 0 1, 0 0 0. How would I do the kernel of this when x1 would be undefined?
    Think about it like this... the identity matrix is really just the identity function and so if v\ker I one has that \bold{0}=Iv=v and so..
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  3. #3
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    One thing it is useful to know- a square matrix is invertible if and only if its kernel contains only the 0 vector.
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