Please solve the attached applied linear algebra question with correct steps and explanations:Thanks Q3Let A be n x n matrix that has zeroson the main diagonal and oneseverywhere else. Example of a 4 x 4matrix of this type is given below111111111111(За,Compute det(A) andA- for n = 2, 3, 4.(3b,Note that in the cases2, 3, 4 the matrix A- has an =6.special structure (all the elements onthe diagonal are the same and all theoff-diagonal elements are also thesame). Guess a formula for A-! inthe general case (or arbitrary n) andverify that your guess is correct bychecking that AA¬! = I.

Answered: Image /qna-images/answer/e2422b70-5135-4ee5-929d-adeff402987c.jpg

Answered: Q3 Let A be n × n matrix that has zeros…

Q3 Let A be n × n matrix that has zeros on the main diagonal and ones everywhere else. Example of a 4 × 4 matrix of this type is given below 1 1 1 1 1 1 1 1 1 1 1 1 0.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 35E: 35. A permutation matrix is a matrix that can be obtained from an identity matrix by interchanging...

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Question

Please solve the attached applied linear algebra question with correct steps and explanations:

Thanks

Q3
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
1
1
1
1
1
1
1
1
1
1
1
1
(За,
Compute det(A) and
A- for n = 2, 3, 4.
(3b,
Note that in the cases
2, 3, 4 the matrix A- has a
n =
6.
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 AA¬! = I.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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