DO NOT USE AI TO ANSWER THE QUESTION! I WILL REPORT YOU IF I FIND OUT.

Exercise 7 (Minimal Polynomials 3; 5 points): We will now ap ply the previous two problems. If oz 2 W, then Q(():) is a three dimensional Qvector space with a basis B = {1,21/3,22/3}. Setting = 3- 21/3 l 5 ' 22/3, nd [Tag and nd its minimal and characteristic polynomial. Use this to find the minimal poly- nomial of B. (Hint: Use the Cayley-Hamilton theorem and the final part of the previous problem)