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.)
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)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....
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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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f19b4e0-ccfa-446a-8524-356ffb42dff2%2F54bc033f-3162-4f8d-9bbf-526d739c93a7%2F5zbtmnd_processed.png&w=3840&q=75)
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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