Assignment For Section 2.5

Readings Questions:

You should read the section before attempting any reading questions or problems. Remember that you are responsible for all definitions and examples. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)   Let   and  .  Show that q(x) is negative definite first without using Sylvester's theorem and then using this theorem (theorem 2.5.2).
 

2)   Consider .

        a)    Show that p(x,y) is positive semi-definite without using Sylvester's theorem.
                Note:   This shows that p(x,y) is not positive definite.

        b)    Show that 

        c)    Why does this not contradict Sylvester's theorem?
 
 
 

Problems:

page 148     1, 3, 4, 7, 10, 13, 15, 17, 20a, 21