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.

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