11. Find a basis for the T-cyclic subspace W of the operator T: V→V generated by the vector 2: V=R³, T(a, b, c) = (a+b+c, 3b, a - c), z = (1,0,0).

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Chapter2: Second-order Linear Odes
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Answer: Basis for W: ((1, 0, 0), (1,0,1)). Characteristic polynomial for Tw: g(t) = t2 - 2.
11. Find a basis for the T-cyclic subspace W of the operator T: V→V generated by the
vector 2:
V=R³, T(a, b, c) = (a + b + c, 3b, a-c), z = (1,0,0).
Then find the characteristic polynomial of the operator Tw ("T restricted on W").
Transcribed Image Text:11. Find a basis for the T-cyclic subspace W of the operator T: V→V generated by the vector 2: V=R³, T(a, b, c) = (a + b + c, 3b, a-c), z = (1,0,0). Then find the characteristic polynomial of the operator Tw ("T restricted on W").
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