Mathematics · Linear Algebra
Let A be an n × n matrix. We say that A is diagonalizable if there exists a nonsingular matrix P such that PAP-1 is a diagonal matrix. Which of the following conditions implies that A is diagonalizable?
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- 1A has n linearly independent eigenvectors✓
- 2A2 is diagonalizable
- 3There exists an integer k such that Ak is nilpotent
- 4There exists an integer k such that Ak = I
Correct answer
A has n linearly independent eigenvectors
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