- #1
Solving Exercise 12 from Hoffman & Kunze's Linear Algebra
- Context: Graduate
- Thread starter asmani
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Discussion Overview
The discussion revolves around solving exercise 12 from Hoffman and Kunze's Linear Algebra, specifically focusing on finding an elementary method to determine the inverse of a certain matrix. Participants are seeking hints and strategies for this problem.
Discussion Character
- Homework-related, Exploratory
Main Points Raised
- One participant asks for the most elementary way to solve the exercise and requests hints.
- Another participant suggests that example 16 might provide small examples that could help in guessing the inverse and proposes proving it through matrix multiplication.
- A similar suggestion is reiterated by another participant, emphasizing the use of examples to guess the inverse.
- A later reply mentions that the original poster has searched online but found stronger results without elementary proofs, indicating a need for a simpler approach to show the matrix is invertible and that the inverse has integer entries.
- The original poster shares that they do not need to prove the inverse matrix itself, only its invertibility.
Areas of Agreement / Disagreement
Participants express a common interest in finding an elementary method for the problem, but there is no consensus on a specific approach or solution. Multiple strategies are suggested, indicating a lack of agreement on the best method.
Contextual Notes
There is an indication that the matrix in question is not named in the book, which may limit the discussion. Additionally, the search for elementary proofs versus stronger results suggests a divergence in the types of solutions being sought.
- #2
Office_Shredder
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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
- #3
AlephZero
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Office_Shredder said:
If you can't guess, Google is your friend.
- #4
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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