# Math Help - Image and Kernel

1. ## 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...

2. 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.