Let A be a 10 x 10 real matrix. Assume that the rank of A is 7. Which of the following statements is necessarily true?
1
There exists a vector v ∈ ℝ10 such that Av ≠ 0 and A2v = 0
2
There exists a vector v ∈ ℝ10 such that A2v ≠ 0
3
A must have a non-zero eigenvalue
4
A7 = 0