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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 61E

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