Consider the quadratic polynomial p: ³ :

a. Express the polynomial in matrix form [2.91]. Make sure your matrix c is symmetric.

b. Apply the Cholesky algorithm to determine if your matrix c is positive definite.

c. Solve for the point x indicated by [2.92].

d. What is the polynomial’s value at the point x obtained in item (c)?

e. Is your solution a maximum, minimum, or saddle point?

a. Expressed in matrix form [2.91], polynomial [2.93] becomes

where

b. Applying the Cholesky algorithm, we obtain Cholesky matrix

We conclude that the matrix c is positive definite.

c. By [2.92]

d. 1

e. Because the matrix c is positive definite, it is a minimum.