Question

Linear Algebra problem.

Let A be an 2x2 matrix over the real numbers.
1. The subset {A^2, A^5, A^11} is always linearly dependant.
2. The subset {I, A, A^2} is always linearly dependant.
3. It is possible that the subset {A^2, A^5, A^11} is linearly independant.
4. It is possible that the subset {I, A^2, A^5, A^11} is linearly independant.
5. It is possible that the subset {I, A, A^2} is linearly independant.


Appreciate your help!

notice I means the identity matrix.

Answer 1

*