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Math Help - Image and Kernel

  1. #1
    Newbie
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    Dec 2008
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    Image and Kernel

    Describe the image and kernel of the transformation geometrically:
    Orthogonal projection onto the plane x+2y+3z=0 in R^3

    Is the image just R^3? No idea how to find the kernel of this...
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  2. #2
    Member eXist's Avatar
    Joined
    Aug 2009
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    The kernel is when en element is taken to the zero element in the image.

    So, say you have a transformation f that takes something from:

    f:S\rightarrow L

    The kernel of this transformation would be:
    \{s \in S \mid f(s) = 0\} where 0 is the zero element in L.

    So in your case, the kernel would be any elements in the orthogonal projection that get mapped to the 0 element.

    Hope this helps a little.
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