Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. An example of a 4 × 4 matrix of this type is given below [0 1 1 1° |1 0 1 1 |1 1 0 1 1 1 1 0 3a)Compute det(A) and A-1 for n = 2, 3, 4. 3b) Note that in the cases n = 2, 3, 4 the matrix A¬1 has a special structure (all the elements on the diagonal are the same and all the off- diagonal elements are also the same). Guess a formula for A¬1 in the general case (or arbitrary 1n) and verify that your guess is correct by checking that AA¬1 = I.
Let A be n x n matrix that has zeros on the main diagonal and ones everywhere else. An example of a 4 × 4 matrix of this type is given below [0 1 1 1° |1 0 1 1 |1 1 0 1 1 1 1 0 3a)Compute det(A) and A-1 for n = 2, 3, 4. 3b) Note that in the cases n = 2, 3, 4 the matrix A¬1 has a special structure (all the elements on the diagonal are the same and all the off- diagonal elements are also the same). Guess a formula for A¬1 in the general case (or arbitrary 1n) and verify that your guess is correct by checking that AA¬1 = I.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
Related questions
Question
![Let A be n x n matrix that has zeros on the main diagonal and ones
everywhere else. An example of a 4 x 4 matrix of this type is given below
0 1 1 1'
1 0 1
1 1 0 1
[1 1 1 0
3a)Compute det(A) and A-1 for n = 2, 3, 4.
3b) Note that in the cases n = 2, 3,4 the matrix A-1 has a special
structure (all the elements on the diagonal are the same and all the off-
diagonal elements are also the same). Guess a formula for A in the
general case (or arbitrary n) and verify that your guess is correct by checking
that AA1 = I.
–1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ae2b3ba-f328-4dc9-b16f-b2cc8c80b86c%2Fa8488dcd-16eb-42a6-bd02-964ee85aaa20%2Fcw5dqg8_processed.png&w=3840&q=75)
Transcribed Image Text:Let A be n x n matrix that has zeros on the main diagonal and ones
everywhere else. An example of a 4 x 4 matrix of this type is given below
0 1 1 1'
1 0 1
1 1 0 1
[1 1 1 0
3a)Compute det(A) and A-1 for n = 2, 3, 4.
3b) Note that in the cases n = 2, 3,4 the matrix A-1 has a special
structure (all the elements on the diagonal are the same and all the off-
diagonal elements are also the same). Guess a formula for A in the
general case (or arbitrary n) and verify that your guess is correct by checking
that AA1 = I.
–1
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