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...

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- Jan 23rd 2010, 02:42 PMSusaludaImage and Kernel
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... - Jan 23rd 2010, 08:36 PMeXist
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.