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.
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?
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