Troubleshooting - A Guide to MATLAB for Beginners and Experienced Users - page 264

U2 =

0.8165 -0.5774 0.7071

0.4082 -0.5774 -0.7071

0.4082 -0.5774 -0.0000

R2 =

2.0000 0 0

0 -1.0000 0

0 0 3.0000

We observe that the columns of U1 are negatives of the corresponding
columns of U2 . Finally,

A*B - B*A

ans =
0

0 0

0 0 0

0 0 0

Problem 13

(a)

If we set X n to be the column matrix with entries x n , y n , z n , and M the
square matrix withentries 1, 1/4, 0; 0, 1/2, 0; 0, 1/4, 1 then X n + 1 = MX n .

(b)

We have X n = MX n − 1 = M 2 X n − 2 = ... = M n X 0 .

(c)

M = [1, 1/4, 0; 0, 1/2, 0; 0, 1/4, 1];
[U,R] = eig(M)

U=

1.0000 0 -0.4082

0 0 0.8165

0 1.0000 -0.4082

R=

1.0000 0 0

0 1.0000 0

0 0 0.5000