Suppose that

(a) Show that the system has a double eigenvalue if and only if the condition (a - d)2 + 4bc = 0 is satisfied, and that the eigenvalue is 1/2 (a + d) .
(b) Show that if the condition in (a) holds and a = d, the eigenspace will be two-dimensional only if the matrix

is diagonal.
(c) Show that if the condition in (a) holds and a ‰  d, the eigenvectors belonging to 4(a + d) are linearly dependent; that is, scalar multiples of

(d) Show that the general solution of the system with double eigenvalue and a ‰  d is

where λ = 1/2(a + d).

Transcribed Image Text:

bd 2b Siet Red 0