Question: Suppose that (a) Show that the system has a double eigenvalue if and only if the condition (a - d)2 + 4bc = 0 is
-1.png)
(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
-2.png)
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
-3.png)
(d) Show that the general solution of the system with double eigenvalue and a ‰ d is
-4.png)
where λ = 1/2(a + d).
bd 2b Siet Red 0
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