Question 1: Let a, b, and c be elements of a field F, and let A be the following 3 x 3 matrix over F:
Prove that the characteristic polynomial for A is x3 - ax2 - bx - c and that this is also the minimal polynomial for A.
Question 2: Let V be a finite-dimensional vector space. What is the minimal polynomial for the identity operator on V? What is the minimal polynomial for the zero operators?
Textbook - LINEAR ALGEBRA (2nd Edition) by KENNETH HOFFMAN, RAY KUNZE.
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