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- Thread starter asmani
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In summary, the conversation is about solving exercise 12 on page 27 of Hoffman and Kunze's book Linear Algebra. The easiest way to solve it is to use examples to guess the inverse and then prove it through matrix multiplication. If unable to guess, Google can be helpful. However, the book does not mention the name of the matrix and only stronger results with insufficient elementary proofs can be found. The goal is to prove that the inverse matrix is invertible with integer entries. Example 16 is provided for reference.

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Office_Shredder

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AlephZero

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Office_Shredder said:

If you can't guess, Google is your friend.

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asmani

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Thanks for the replies.

I've searched by Google (actually the book doesn't mention the name of the matrix), and all I found is some stronger results (like in Wikipedia: http://en.wikipedia.org/wiki/Hilbert_matrix) with not enough elementary proofs. I don't need to prove what the inverse matrix is, just need to prove it is invertible, and the inverse has integer entries.

Here is the example 16:

I've searched by Google (actually the book doesn't mention the name of the matrix), and all I found is some stronger results (like in Wikipedia: http://en.wikipedia.org/wiki/Hilbert_matrix) with not enough elementary proofs. I don't need to prove what the inverse matrix is, just need to prove it is invertible, and the inverse has integer entries.

Here is the example 16:

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blue_raver22

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I am familiar with Hoffman and Kunze's book and its exercises. Exercise 12 on page 27 asks for the most elementary way to solve a given problem. The best approach to solving this exercise would be to first review the basic concepts and definitions of linear algebra, such as vectors, matrices, and basic operations like addition and multiplication. Then, carefully read and understand the given problem and its requirements. Next, try to break down the problem into smaller, more manageable steps. This will help in finding the most efficient and elementary way to solve it. Additionally, consulting other resources, such as online tutorials or asking for hints from peers or a teacher, can also aid in finding a solution. Remember to always check your work and make sure it aligns with the given problem and its solution. I wish you the best of luck in solving this exercise.

Exercise 12 serves as a review of the concepts and techniques learned in previous chapters of the textbook. It also challenges the reader to apply their understanding of linear algebra to solve more complex problems and develop problem-solving skills.

Exercise 12 covers a variety of topics including vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, and inner product spaces. It also includes exercises on solving systems of linear equations and solving problems using matrices.

It is recommended to first review the relevant concepts and techniques covered in previous chapters. Then, carefully read each problem and identify the key concepts and techniques needed to solve them. Work through the problems step by step, and don't hesitate to consult the textbook or other resources if you get stuck.

While completing the exercises in a textbook is not always necessary, it can greatly enhance your understanding and mastery of the subject. Exercise 12 in Hoffman & Kunze's Linear Algebra covers important concepts and techniques that are essential for a thorough understanding of linear algebra.

Aside from the textbook itself, there are many online resources such as video tutorials, practice problems, and study guides that can aid in solving Exercise 12. It may also be helpful to consult with a teacher or tutor if you are struggling with any particular problems.

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