Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in H whose sum is not in H, using a comma separated list and2] [5syntax such as [[1,2], [3,4]], [[5,6],[7,8]] for the answer(Hint: to show that H is not closed under addition, it issufficient to find two nilpotent matrices A and B such that (A+B)" +0 for all positive integers n.)Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a matrix in H whose product is not in H, using[3 4]a comma separated list and syntax such as 2, [[3,4], [5,6]] for the answer 2,[5 6(Hint: to show that H is not closed under scalarmultiplication, it is sufficient to find a real numberr and a nilpotent matrix A such that (rA)" +0 for all positive integers n.)

Answered: Image /qna-images/answer/1e3792db-5b5a-4de9-a362-e44ae8199575.jpg

Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in H whose sum is not in H, using a comma separated list and [1 2] [5 6] 3 syntax such as [[1,2], [3,4]], [[5,6],[7,8]] for the answer (Hint: to show that H is not closed under addition, it is 8 sufficient to find two nilpotent matrices A and B such that (A + B)" # 0 for all positive integers n.)

Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in H whose sum is not in H, using a comma separated list and [1 2] [5 6] 3 syntax such as [[1,2], [3,4]], [[5,6],[7,8]] for the answer (Hint: to show that H is not closed under addition, it is 8 sufficient to find two nilpotent matrices A and B such that (A + B)" # 0 for all positive integers n.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in H whose sum is not in H, using a comma separated list and
2] [5
syntax such as [[1,2], [3,4]], [[5,6],[7,8]] for the answer
(Hint: to show that H is not closed under addition, it is
sufficient to find two nilpotent matrices A and B such that (A+B)" +0 for all positive integers n.)
Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a matrix in H whose product is not in H, using
[3 4]
a comma separated list and syntax such as 2, [[3,4], [5,6]] for the answer 2,
[5 6
(Hint: to show that H is not closed under scalar
multiplication, it is sufficient to find a real numberr and a nilpotent matrix A such that (rA)" +0 for all positive integers n.)

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