Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 5 - Eigenvalues and Eigenvectors - 5.3 Exercises - Page 289: 26

Answer

Yes

Work Step by Step

A is not diagonalizable if the remaining eigenspace is only 1 dimensional. In that case, it would not be possible to form the invertible matrix P because it would have only 6 linearly independent vectors when 7 are needed. It is possible to diagonalize A if the remaining eigenspace is 2 dimensional.
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