I have figured out part a. Part b is giving me trouble.

A real symmetric matrix A -A7 is positive definite if any of the following equivalent conditions hold: The quadratic form is positive for all nonzero vectors All determinants formed from symmetric submatrices of any order cen- tered on the diagonal of A are positive All eigenvalues (A) are positive. . There is a real matrix R such that A-RTR These conditions are difficult or expensive to use as the basis for checking if a particular matrix is positive definite. In MATLAB, the best way to check positive definiteness is with the chol function. See help chol (a) Which of the following families of matrices are positive definite? M magic(n) hilb(n) P pascal(n) I eye(n,n) R randn (n,n) R-randn (n,n); AR' R R-randn (n,n); AR' + R R-randn(n,n); Ieye (n,n); A-R' R n*I (b) If the matrix R is upper triangular, then equating individual elements in the equation A -RR gives ! Using these equations in different orders yields different variants of the Cholesky algorithm for computing the elements of R. What is one such algorithm? A real symmetric matrix A -A7 is positive definite if any of the following equivalent conditions hold: The quadratic form is positive for all nonzero vectors All determinants formed from symmetric submatrices of any order cen- tered on the diagonal of A are positive All eigenvalues (A) are positive. . There is a real matrix R such that A-RTR These conditions are difficult or expensive to use as the basis for checking if a particular matrix is positive definite. In MATLAB, the best way to check positive definiteness is with the chol function. See help chol (a) Which of the following families of matrices are positive definite? M magic(n) hilb(n) P pascal(n) I eye(n,n) R randn (n,n) R-randn (n,n); AR' R R-randn (n,n); AR' + R R-randn(n,n); Ieye (n,n); A-R' R n*I (b) If the matrix R is upper triangular, then equating individual elements in the equation A -RR gives ! Using these equations in different orders yields different variants of the Cholesky algorithm for computing the elements of R. What is one such algorithm