Describe the image and kernel of the transformation geometrically:
Orthogonal projection onto the plane x+2y+3z=0 in $\displaystyle R^3$
Is the image just $\displaystyle R^3$? No idea how to find the kernel of this...
The kernel is when en element is taken to the zero element in the image.
So, say you have a transformation $\displaystyle f$ that takes something from:
$\displaystyle f:S\rightarrow L$
The kernel of this transformation would be:
$\displaystyle \{s \in S \mid f(s) = 0\}$ 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.