Question Two Suppose that A is an n x n matrix such that 4² = 0. a) Show that if € im(A), then € null(A). (In other words, show that im(A) C null(A).) b) Is it necessary that if ✔ € null(A) then € im(A)? (Either provide a proof, or show that this is not necessary.)

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 29CM
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Question Two
Suppose that A is an n x n matrix such that A² = 0.
a) Show that if € im(A), then € null(A). (In other words, show that im(A) C null(A).)
b) Is it necessary that ifnull(A) then im(A)? (Either provide a proof, or show that this is not necessary.)
Transcribed Image Text:Question Two Suppose that A is an n x n matrix such that A² = 0. a) Show that if € im(A), then € null(A). (In other words, show that im(A) C null(A).) b) Is it necessary that ifnull(A) then im(A)? (Either provide a proof, or show that this is not necessary.)
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