Here is the homework assignment. It is designed to give you experience with the QZ decomposition. You can get the software you need below:

Here are QZDIV.M and QZSWITCH.M, programs written by Chris Sims. To get the QZ decomposition of a and b, where

QaZ=H0, QbZ=H1,

where H0 and H1 are upper triangular and the zeros on the diagonal of H0 are concentrated in the lower right, run the following commands:

 [H0,H1,q,z,v]=qz(a,b);
 stake1 = 1e+08;
stake2 = 1e-05;
[H0,H1,q,z] = qzdiv(stake1,H0,H1,q,z);

qz is a MATLAB program, and qzdiv.m calls qzswitch.m. Verify, ex post, that the routine is providing you with what you want. That is, verify that H0 and H1 are upper triangular, with the zeros of H0 being in the lower right. Also, verify that QaZ=H0, and QbZ=H1, and that Q and Z are orthonormal.