Question

Let T : R10 → R10 be a linear operator on R10. Suppose that R10 is decomposable into the direct sum of two T-invariant subspaces W1 and W2. Let ∆i(t) and mi(t) be the characteristic and minimal polynomials, respectively, of the restriction of the operator T to Wi for i = 1, 2. Suppose ∆1(t) = m1(t) = (t + 1)6(t − 3), ∆2(t) = (t − 3)3, m2(t) = t − 3; u = (−1, 5, 0, . . . , 0) ∈ W2.
Find the following (briefly justify your answer!):
(a) the characteristic polynomial of T,
(b) the minimal polynomial of T,
(c) the Jordan form of T,
(d) dim W1,
(e) T(u).

Answer 1

Answer:

And I have to make a difference between us in correct I have to make a difference between us in correct I have to make a difference between us in correct I have to make a difference between us in correct I have to make a difference between us in correct✅