Matrices in Mathematica -- How to calculate eigenvalues, eigenvectors, determinants and inverses?

In summary, the conversation was about a bonus assignment involving the use of Mathematica to calculate matrices and their determinants. The person is a beginner with Mathematica and was able to complete some tasks, but is having trouble with task d and getting an error. They are seeking help from others and were able to use a trick to plot the eigenvalues for different values of n without repeating the calculation.
  • #1
Lambda96
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TL;DR Summary
How to calculate eigenvalues, eigenvectors, determinants and inverses of a general nxn matrix
Hi,

In my linear algebra homework, there is a bonus assignment where we are supposed to use Mathematica to calculate matrices and their determinants etc. here is the assignment.

Bildschirmfoto 2023-05-17 um 15.02.04.png


Unfortunately, I am a complete newbie when it comes to Mathematica, this is the first time I have worked with Mathematica.

I was able to calculate the task a to c. Here is the solution for task b and the Matrix for the case ##n=5##.
Bildschirmfoto 2023-05-17 um 18.58.17.png

I have now problems with the task d, where I should calculate the determinants, eigenvalues, etc for the general case n or rather give a formula.

For the determinant as an example I proceeded as follows and unfortunately I get the following error:

Bildschirmfoto 2023-05-17 um 18.59.47.png

Unfortunately I don't know how to fix the error or is my initial equation already wrong?
 
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  • #2
You can't leave n undefined. Mathematica can't find the rule for arbitrary n by itself. You have to calculate the result for explicit values of n, and then find by yourself the general rule.
 
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Likes Lambda96 and renormalize
  • #3
As DrClaude says, ##n## must be specified explicitly:
1684346274397.png

The pattern is pretty obvious.
 
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Likes DrClaude and Lambda96
  • #4
Thanks DrClaude and renormalize for your help 👍👍

Thanks also renormalize for the trick with plotting n objects in Mathematica, so I could directly plot the eigenvalues from ##n=1## to ##n=10## without repeating the calculation 10 times 👍

I could now recognize corresponding patterns for the other values :smile:
 
  • Like
Likes renormalize and DrClaude

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