True or False. If the statement is true, prove it. Otherwise, give a counterexample. 1. Let A, B ∈ M_n(F). If nullity(A) = nullity(B) then A and B are similar. 2. The function L : M_n(F) → M_n(F) defined by L(A) = A − A^T is a linear transformation. 3. All nonzero linear transformations T : F^3 → F are onto.

True or False. If the statement is true, prove it. Otherwise, give a counterexample. 1. Let A, B ∈ M_n(F). If nullity(A) = nullity(B) then A and B are similar. 2. The function L : M_n(F) → M_n(F) defined by L(A) = A − A^T is a linear transformation. 3. All nonzero linear transformations T : F^3 → F are onto.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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