Let A be an n×n symmetric positive definite matrix (i.e. for any non-zero column vector w, wTAw > 0). If we write A as A = [a bT b C ] where a is the (1, 1) entry of A, b is an (n − 1) × 1 column vector, bT is the transpose of b and C is an (n − 1) × (n − 1) matrix. Find x > 0, y and Z, such that A =[x 0 * [1 0 * [x yT y I ] 0 Z ] 0 I] where y is a column vector of length n − 1 and Z is an (n − 1) × (n − 1) matrix. Show that Z is also symmetric positive definite.

I only want to ask how to show Z is also symmetric positive definite matrix.