CSIR NET June 2023 Linear Algebra, Question ID 704030, Let A be a 3x3 real matrix whose character...

Linear Algebra
Mathematical Science
Part-B Question, CSIR NET June 2023 Exam.
Question ID 704030: Let A be a 3x3 real matrix whose characteristic polynomial p(T) is divisible by T^2. Which of the following statements is True?

(1) The eigenspace of A for the eigenvalue 0 is two-dimensional.
(2) All the eigenvalues of A are real.
(3) A^3=0
(4) A is diagonalizable.

We have found the correct solution. Option (2) is correct.

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