Consider the following family of n x n matrices: sIn-1 a aT S2 2 (b) For n = 4 and a (c) Extra credit: What $1 1 1)? a = 1 (1 n ... Pn where a R-1. (a) For which vectors a E Rn-1 will Pn be positive definite? (Hint: Schur comple- ment.) = = 9 $1 (1 1 1) determine the Cholesky decomposition of P. can you say about the Cholesky decpomosition of Pn for