Describe the kernel and range of (a) the orthogonal projection on the xz -plane (b) the orthogonal projection on the yz-plane (c) the orthogonal projection on the plane defined by the equation y=x

Question

anonymous · Answer

Just looking at (a), the range is obviously the vectors in the xz plane, right?  And can you think of which vectors would have no projection in the xz plane?

anonymous · Answer

I have no idea what to do. So if you could show the first one it would be great

anonymous · Answer

An orthogonal projection maps a vector to its "shadow" on a given plane, like this:
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