Let V be a finite-dimensional real vector space and T1, T2 be two nilpotent operators on V. Let W1 = {v ∈ V : T1(v) = 0} and W2 = {v ∈ V : T2(v) = 0}. Which of the following statements is FALSE?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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If W1 and W2 are isomorphic vector spaces, then T1 and T2 must have the same minimal polynomial.

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Answer 1

If T1 and T2 are similar, then W1 and W2 are isomorphic vector spaces.

Answer 2

If W1 and W2 are isomorphic vector spaces, then T1 and T2 must have the same minimal polynomial.

Answer 3

If W1 = W2 = V, then T1 and T2 are similar.

Answer 4

If W1 and W2 are isomorphic, then T1 and T2 have the same characteristic polynomial.

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