hwk3.1 - due Tues 2/12

Bretscher 7.1#8,9,12,15(except the part about finding a basis),38,54ab(but not c)
As you work 54, compare to our version of the lilac bush from lecture and from last Friday's homework.  The rules of growth differ, so they will behave differently.  

Let's revisit Friday's lilac bush problem in light of what we know now.  Using what you know now, but without doing any new work, can you find an eigenvector for Friday's lilac bush problem?  (The numbers are not as nice, but write down your best estimate.  Now, multiply this vector by A to check that it really is an eigenvector).

Bretscher 2.1 #42,43,44,47,51a

2.1#1-3(if the transformation is linear, find the matrix that does it)
2.2#4,8,9(for each of these, find all eigenvectors.  Hint: In one case, there are 2 distinct "types" of eigenvectors.  In another case, there is only 1 "type".  In another, there are 0 "types".)