Inverse of upper/lower triangular matrix

  • Thread starter Jamin2112
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  • #1
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Homework Statement



screen-capture-37.png


Homework Equations



From my course notes:

screen-capture-1-23.png


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?
 

Answers and Replies

  • #2
Stephen Tashi
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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.
 
  • #3
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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.

So there's no magical formula?
 
  • #4
Stephen Tashi
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Using the adjugate is a magical formula. How else can we explain it?
 
  • #5
Stephen Tashi
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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?
 
  • #6
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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.
 
  • #7
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So I did it the lame way:

screen-capture-1-24.png






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?



screen-capture-2-13.png
 

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