A be a 3 x 3 matrix with eigenvalues M_i and corresponding linearly independent eigenvectors xi, i = 1,2,3. Suppose M1= M2. Choose the true statement from (i), (ii), (iii) below and give an explanation for your answer.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 29E
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Let A be a 3 x 3 matrix with eigenvalues M_i and corresponding
linearly independent eigenvectors xi, i = 1,2,3. Suppose M1= M2.
Choose the true statement from (i), (ii), (iii) below and give an
explanation for your answer.
(i) A can be diagonalized.
(ii) A cannot be diagonalized.
(iii) I need more information to decide.

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