3. Let A be n × n matrix that has zeros on the main diagonal and ones everywhere else. Example ofa 4 x 4 matrix of this type is given below111111111111(3a) Compute det(A) and A- for n = 2, 3, 4.(3b) Guess a formula for A- in the general case and verify that your guess is correct by checkingthat AA-l = I.

Answered: Image /qna-images/answer/b6f7777c-ff15-48cd-8a86-9a6625883a3b.jpg

3. Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. Example of a 4 x 4 matrix of this type is given below 0. 1 1 1 1 1 1 1 1 1 1 1 1 (3a) Compute det(A) and A-1 for n = 2, 3, 4. %3D (3b) Guess a formula for A- in the general case and verify that your guess is correct by checking that AA-l = I.

3. Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. Example of a 4 x 4 matrix of this type is given below 0. 1 1 1 1 1 1 1 1 1 1 1 1 (3a) Compute det(A) and A-1 for n = 2, 3, 4. %3D (3b) Guess a formula for A- in the general case and verify that your guess is correct by checking that AA-l = I.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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