Question

Define T : R 3 → R 3 by T(x, y, x) = (x+y, y,2x−2y+2z). Check that T satisfies the polynomial (x−1) 2 (x−2). Find the minimal polynomial of T. ?

Answer 1

See below.

Explanation:

With

`T = ((1,1,0),(0,1,0),(2,-2,2))`

we have

`(T-I_3)^2(T-2I_3) = 0_3` and the characteristic polynomial is obtained as

`p(lambda) = det(T-lambda I_3) = (lambda-1)^2(lambda-2)`