470 Apprritlix A Soltitions to tlic Excrcisc.:, e==[ 13-8j 13tsj d=2 The cigenvalues of the system air -2 T-j (equal t,o the diagonal elements of d) Thc systcm does not ckimge its input-output hrliavior with thr tramformalion from Eq 2.47 - 2.50 c) It, i s conLrollaI.)le as all elmwits of b are non-zero aiitl it is ohscrvable a.; all c.lernents of i: arc iion-zero 0 0 I b) The proof i s easy if one recognises that left niultiplication with 1C-l can be intrrprf>tcdits horizontally mirroring the matrix elrinc'nts, and right iiiiiltiplication with T as vertical mirroring Solution 3.1 Solution 3.2 a ) yes, b) no, c) no, (1) 110, e) yes, as H ( = j ) = Solution 3.3 a) Corisistmt norrrialisation for t hc components: This yields Lhe iiorinalised component v:ihic+x R - 1; C = - L = 1.2 6'