Geometric description of a kernel

[eyehategod]

let T:R$$^{3}$$ $$\rightarrow$$ R$$^{3}$$ 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?

 

[Dick]

That's pretty vague. Thinking about dimensions would be a good start.

 

[HallsofIvy]

let T:R$$^{3}$$ $$\rightarrow$$ R$$^{3}$$ 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?

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.