20 September 2014
1) Find all (complex) characteristic values and characteristic vectors of the following matrices:
- 1 1 1 (b) 1 1 1
1 1 1 0 1 1
1 1 1 0 0 1
2) Let T be the linear operator on R3 which is represented in the standard basis by the matrix
-9 4 4
-8 3 4
-16 8 7
Prove that T is diagonalisable.
3) Show that similar matrices have the same minimal polynomial.
