Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Engineering Mathematics Linear Algebra Eigenvectors
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 imply that A is diagonalizable?
1
There exists integer k such that Ak = I
2
There exists integer k such that Ak is nilpotent
3
A2 is diagonalizable
4
A has n linearly independent eigenvectors
5
Question Not Attempted