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Geometric description of a kernel

  1. Nov 11, 2007 #1
    let T:R[tex]^{3}[/tex] [tex]\rightarrow[/tex] R[tex]^{3}[/tex] be a linear transformation.
    how can i figure out a geometric description of the kernel and range of T. What do I have to look at?
  2. jcsd
  3. Nov 11, 2007 #2


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    That's pretty vague. Thinking about dimensions would be a good start.
  4. Nov 12, 2007 #3


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    For a general linear transformation, about the most you can say are that the kernel and range are both subspaces (if they are not trivial). For different the kernel might be {(0,0,0)}, a line through (0,0,0), a plane through (0,0,0), or all of R3. Same for the range.
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