I've just started the Eigenvector section. In Example 1(p. 284) the answer given for the first Eigenvector is (.6 , .4). However, it seems the natural way to calculate this would result in the answer (3/2 , 1). The two answers are equivalent, but I'm wondering why he chose an answer in a form the student would not immediately get. Was it the fact that .6 + .4 = 1? 1 also happened to be the corresponding eigenvalue. Anyone know?

Question

I've just started the Eigenvector section. In Example 1(p. 284) the answer given for the first Eigenvector is (.6 , .4).  However, it seems the natural way to calculate this would result in the answer (3/2 , 1). The two answers are equivalent, but I'm wondering why he chose an answer in a form the student would not immediately get.  Was it the fact that .6 + .4 = 1?  1 also happened to be the corresponding eigenvalue. Anyone know?

anonymous · Answer

Well, if you look a bit ahead, you'd come across Markov matrices where the columns add up to 1. And, you'd also see that Markov matrices always have one eigenvalue = 1 (and, other eigenvalues have magnitude <= 1; equal to 1 only in special cases as Prof. Strang explains in his lecture). So, in this example 1 (on page 284), the matrix A is indeed a Markov matrix.... 
Personally, I would have preferred an easier (whole number) example to begin with, but that's just me :-)

datanewb · Answer

Ahh, that's why.  Yes, since I posted the question I've run across those Markov matrices.  Thanks!