a11 a12 a13 The matrix A = a21 a22 a23 = a31 a32 a33 [3-2 0 det 9 -1-2 2 = -9 4 -1-2 -23+( )2+( 301 9-12 -94-1 has characteristic equation )2+( )= 0. The eigenvalue with positive imaginary part is = + For eigenvalue 1, the eigenvector has components a, b and c that satisfy (3-1)a+(0)b + (1)c = 0, (9)a+(-11)b + (2)c = 0, (-9)a+(4)b+(-1-2)c=0 which is the system [ + i]a+ b+ c = 0, a+[ + i]b+ c = 0, a+ b+[ + i]c = 0 Choosing the first component of the eigenvector as a = 1, this eigenvector is --8-8- b where b = + i and c = i +