I. Answer "True" or "False" for each statement. If the statement is "true," provide justification (proof) for your answer. If the statement is "false," provide a counter example that would be true. i. For a linear transformation T : V → V it holds that [T(7)]a = [T(w)]. for any basis a if w + (-ü) is in ker(T). ii. If A is a square matrix, the span of any of its eigenvectors creates an eigenspace of A. iii. If Y is a solution to a differential system Y' = AY+G, for constant Gnx1 and Anxn, then Y" = (Y')' exists and Y is also a solution to Y" = A?Y .

I. Answer "True" or "False" for each statement. If the statement is "true," provide justification (proof) for your answer. If the statement is "false," provide a counter example that would be true. i. For a linear transformation T : V → V it holds that [T(7)]a = [T(w)]. for any basis a if w + (-ü) is in ker(T). ii. If A is a square matrix, the span of any of its eigenvectors creates an eigenspace of A. iii. If Y is a solution to a differential system Y' = AY+G, for constant Gnx1 and Anxn, then Y" = (Y')' exists and Y is also a solution to Y" = A?Y .

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 18EQ

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