# Exercise Solution 2.10

- The Cholesky algorithm yields the matrix
[s1]

Because the algorithm completes successfully with no 0 diagonal elements, the original matrix is positive definite.

- At the fifth step of the Cholesky algorithm, we obtain
[s2]

where

*x*is indeterminate. We set*x*equal to 0 and proceed. We obtain the matrix[s3]

Because this has a 0 diagonal element, we conclude that the original matrix is singular positive semidefinite.

- The Cholesky algorithm fails in the final step, calling for a square root of –1. The matrix is neither positive definite nor singular positive semidefinite.