One method for Eigenvalues does not work

[sfan]

Greeting, everyone

With the first approach, Mathcad cannot return to a solution. But the second one using Polyroots works.

And when I check with the eigenvalues derived from above, the determinant is not equal to 0, why?

Thank you for your time.

Best

Shawn

[sfan]

Sorry I forget to upload the file.

But this time it is still a 3.1 version.

[AlanStevens · Accepted solution]

Are you sure it can't be solved, or is it just that it can't be displayed (which is the situation in Mathcad 15)?  If the latter try replacing one of your integers by a floating point number as in my (M15) picture below (I can't test your file as I don't have Prime 3.1).  Note that I've replaced the 1 in your M matrix by 1.0.

Alan

[sfan]

Yes, Alan

Take the float to 3 for instance will display the solution.

But any thought on the the fact that the determinant is not equal to zero?

Thank you

Shawn

[AlanStevens]

Shawn Fan wrote:

Yes, Alan

Take the float to 3 for instance will display the solution.

But any thought on the the fact that the determinant is not equal to zero?

Thank you

Shawn

Just limited numerical precision - especially if you use float 3.  This not only limits the display, but, much more importantly, limits the precision of the intermediate calculations also.  Below, I've used float 50. 

Alan

[sfan]

Oh, that's right.

Now I know how the float plays. I used to think it just limit the display.

Thank you So Much!