[BDFL_Xenu]

Well, SICP was a printed book before being put on the web (as it is quite a few years older than it), and the version you see on the webpage is just a rendition of it in HTML. Still, I didn't know until today that you could link to individual figures and exercises, it will be even more fun to cite it in a quasi-religious, trollish way.

Also, you generalized the principle (and fused two exercises of the book in one :), or at least I'll have to believe you ;) I didn't form really much of an intuition on eigenvectors during the completely proper Linear Algebra course that I took, which is only my fault.

But I think that the exercise serves to reinforce the underlying theme that with enough attention, one can either supply or draw the insight to chip away yet one more part of the problem, to attack it from another angle, to pull it from just another direction that one had not seen before. It celebrates cleverness and knowledge, used to make complex things simple, to find the easy way out the hard way and end up better in the end, and that's partly why it's so cherished, but we all know that.