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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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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