Question: Matrix A is factored in the form PDP . Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.

Matrix A is factored in the form PDP . Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 2 0 -18 -6 0 - 1 5 0 0 0 0 1 A = 9 5 54 = 0 1 3 0 50 3 18 0 0 5 0 0 0 2 - 0 -6 . . . . . Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 1 = . A basis for the corresponding eigenspace is { } O B. In ascending order, the two distinct eigenvalues are My = and 2 = Bases for the corresponding eigenspaces are { } and { }, respectively. O C. In ascending order, the three distinct eigenvalues are M = , 12 = and 23 = Bases for the corresponding eigenspaces are { }, { }, and { }, respectively
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