(a) Show that the matrix has the repeated eigenvalue r = 2
Chapter 9, Problem 37E(choose chapter or problem)
(a) Show that the matrix has the repeated eigenvalue r = 2 with multiplicity 3 and that all the eigenvectors of A are of the form u = s col(1, 0, 0).(b) Use the result of part (a) to obtain a solution to the system x’ = Ax of the form x1 (t) = e2tu1.(c) To obtain a second linearly independent solution to Hint: Show that u1 and u2 must satisfy (d) To obtain a third linearly independent solution to x’ = Ax, try Hint: Show that u1, u2 and u3 must satisfy (e) Show that
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