Solving Exercise 12 from Hoffman & Kunze's Linear Algebra

[asmani]

Hi all.

From Hoffman and Kunze's book Linear Algebra, page 27, exercise 12:

What's the most elementary way to solve this?

Any hint is appreciated.

 

[Office_Shredder]

Does example 16 calculate several small examples of these? The easiest way might be to use the examples to guess what the inverse is and then just prove through matrix multiplication that it works

 

[AlephZero]

Does example 16 calculate several small examples of these? The easiest way might be to use the examples to guess what the inverse is and then just prove through matrix multiplication that it works

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

 

[asmani]

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:

 

[blue_raver22]

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.