## 18.06 Spring 2006 : Problem Set #5

### due 4PM Wednesday 3/22

(Asterisk means the solution is in the back of the book)

Section 4.3: 1*, 12, 17, 26*, 27

Section 4.4: 3*, 7, 15*, 18*, 24

Section 5.1: 3, 12, 15*, 28, 34*

Computer Problem: Take a reasonably general looking
symmetric 2x2 and also a 3x3 matrix and save them somewhere
for later reference. Apply Gram-Schmidt using the qr algorithm
by [Q,R]=qr(A). Then form A=R*Q. Again do [Q,R]=qr(A) and
A=R*Q. Do this as many times as necessary to make A diagonal
or close to diagonal. Compare the prod(diag(A)) and the
sum(diag(A)) with det(original A) and the sum(diag(original A))
respectively.
The numbers on the diagonal are known as the eigenvalues of A: we
will see these numbers soon officially in our class.

* Copyright © 2003 Massachusetts Institute of
Technology*