Inverse of upper/lower triangular matrix

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    Inverse Matrix
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Homework Help Overview

The discussion revolves around the properties and methods for finding the inverse of upper and lower triangular matrices. Participants are exploring the implications of matrix entries and the use of the adjugate matrix in this context.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the role of diagonal entries and the "little stars" in the matrix inverse. There are discussions about the adjugate matrix and whether it constitutes a straightforward method or a more complex approach. Some suggest visualizing the process through elementary row operations as an alternative method.

Discussion Status

There are multiple lines of reasoning being explored, including the use of the adjugate matrix and elementary row operations. Participants are actively engaging with each other's ideas, but there is no explicit consensus on the best approach or method to use.

Contextual Notes

Some participants reference course materials that may provide additional insights, but there are indications of uncertainty regarding the completeness of the information available to them.

Jamin2112
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Homework Statement



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Homework Equations



From my course notes:

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The Attempt at a Solution



I'm a little confused. I see that all the diagonal entries are inverted, but I'm not sure what's going on with the little stars. Do I have to solve for those?
 
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You can solve for the little stars. Your materials should have information about how to form the inverse of a matrix by using the "adjugate" matrix and the determinant.
 
Stephen Tashi said:
You can solve for the little stars. Your materials should have information about how to form the inverse of a matrix by using the "adjugate" matrix and the determinant.

So there's no magical formula?
 
Using the adjugate is a magical formula. How else can we explain it?
 
You can visualize how the matrices in the problem could be formed using "elementary row operations" on the identity matrix. That might suggest another approach to finding the inverses. Do your materials have notes on that?
 
Stephen Tashi said:
You can visualize how the matrices in the problem could be formed using "elementary row operations" on the identity matrix. That might suggest another approach to finding the inverses. Do your materials have notes on that?


By "magical" I meant no row operations.
 
So I did it the lame way:

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Notice that m1 and m2 are simply negated.

Now that I think of it, there was another part of the notes that mentioned how to do this with a LOWER triangular matrix. I guess it went without saying that it works just as well for upper triangular matrices?



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