Key to MATLAB Exercise 4 School of Mathematical Sciences Xiamen Univer http:/edjpkc.xmu.ed >>A=2 1; -2 1: v, d=eig(A): B=v'sqrt(d)*inv(v) 1.51190.3780 -0.75591.1339 B= 2.000010000 2.000 1.0000 The key to 2)is omitted 6 > format rational; A=01-1; 120: -103: >> U, T=schur(A) 1661/6691-1573/4601 1573/4601 755/833-1661/6691 1661/66911573/4601 755/833 T 655/1006 0 00 665/1172 0 2874/851 >>A=[ll:2310; >>u,S, v]=svd(A) -0.35830.2312-0.9045 -0.9208-0.24740.3015 -0.15410.94090.3015 3.9090 00.8485 0.60220.7983 -0.7983-0.6022 > Singular ValuesOfA=diag(s) 3.9090 0.8485 > RootofAA-roots(poly(A*A)) Rootofaa= 15.2801 0.7199 Key to Ex4-4Key to MATLAB Exercise 4  School of Mathematical Sciences Xiamen University  http://gdjpkc.xmu.edu.cn  Key to Ex4­4  5． 1) >> A=[2 1;­2 1]；[v, d]=eig(A)；B= v*sqrt(d)* inv(v) B =  1.5119  0.3780  ­0.7559  1.1339  >> B*B ans =  2.0000  1.0000  ­2.0000 1.0000  The key to 2) is omitted.  6． >> format rational; A=[0 1 ­1;1 2 0;­1 0 3];  >> [U, T]=schur(A) U =  ­755/833  1661/6691  ­1573/4601  1573/4601  755/833  ­1661/6691  ­1661/6691 1573/4601  755/833  T =  ­655/1006 0  0  0  2665/1172 0  0  0  2874/851  7． >> A=[1 1;2 3;1 0];  >> [u, s, v]=svd(A) u =  ­0.3583  0.2312  ­0.9045  ­0.9208  ­0.2474  0.3015  ­0.1541  0.9409  0.3015  s =  3.9090  0  0  0.8485  0  0  v =  ­0.6022  0.7983  ­0.7983  ­0.6022  >> SingularValuesOfA = diag(s)  SingularValuesOfA =  3.9090  0.8485  >> RootOfAA=roots(poly(A’*A)) RootOfAA =  15.2801  0.7199