Homework #5, MATH 461, Spring 2006

MATLAB Problem Set 5 (due Monday April 24 in section)

Please note the general information for MATLAB assignments, addressing format and collaboration.

This problem set has no problem with randomized numbers, so you can discuss very fruitfully. Produce (and understand) your own input and output.

PROBLEM 1.
6.2: 35 (from Lay's text)
PROBLEM 2.
6.2: 36a (from Lay's text)
PROBLEM 3.
(a) Use the MATLAB command roots(p) to compute the roots of the polynomial
    x^4 - (1.5)x^3 - 6x^2 +2x - .34 .
(b) Use MATLAB to find the eigenvalues of the matrix
    A = [0,1,0,0;0,0,1,0;0,0,0,1; .34 , -2 , 6 , 1.5 ] .
(c) What is the characteristic polynomial of A? Explain.
(d) Suppose for some numbers a,b,c,d,e,f you have the following 6x6 matrix B:
   0     1    0 0    0     0
   0     0    1 0    0     0
   0     0    0 1    0     0
   0     0    0 0    1     0
   0     0    0 0    0     1
-f -e -d -c - b -a

What do you expect to be the characteristic polynomial of B?