True or false:
1) Every transformation T: Cn --> Cn (n ≥ 2) has n distinct eigenvectors
2) Every transformation T: Cn --> Cn (n ≥ 2) has at least 1 eigenvector
3) Every transformation T: Rn --> Rn (n ≥ 2) has at least 1 eigenvector
4) Every transformation T: Rn --> Rn (n ≥ 3) has at least 1 eigenvector
i believe 3 and 4 are both false because not all matrices are diagonalizable so you can't say that those statements are always true but i'm not completely confident