What is the Basis for a Row Reduced 3x3 Matrix in Linear Algebra?

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SUMMARY

The discussion centers on the process of row reducing a 3x3 matrix A to the identity matrix in linear algebra. Participants emphasize the importance of understanding complex eigenvalues and the operation A - λI, where λ represents the eigenvalue. The conversation also touches on the appropriateness of contest-type questions in academic forums, highlighting that such questions are generally discouraged. Overall, the key takeaway is the necessity of diagnosing the matrix over complex numbers to determine its basis effectively.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically matrix operations
  • Familiarity with eigenvalues and eigenvectors
  • Knowledge of row reduction techniques for matrices
  • Basic comprehension of complex numbers and their properties
NEXT STEPS
  • Study the process of row reducing matrices using Gaussian elimination
  • Learn about the implications of complex eigenvalues in matrix theory
  • Explore the relationship between eigenvalues and the determinant of a matrix
  • Investigate the use of the characteristic polynomial in finding eigenvalues
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This discussion is beneficial for students and professionals in mathematics, particularly those studying linear algebra, as well as educators seeking to understand the nuances of contest-type questions in academic settings.

fellupahill
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Long story. Not a homework question, tho sometimes I think the person running the contest would think to use a forum contest to do his coursework. But it's not.

Topic: Linear algebra.

If no one gets it right after 3 days then we can use any means to get the question right, now becomes a race.

Row reduce a 3x3 matrix A to the identity matrix.What is a basis for the matrix?
hint:
(Diagnose a 3x3 matrix over complex numbers and 2 of the complex eigenvalues are row reducing to identity matrices when you do A-lambda*I (where lambda is the eigenvalue

Not copied directly, doing on my phone so sorry for the terrible grammar. And I can't, well more like I don't want to, tell you the prize of the contest, its super nerdy and embarrassing. Maybe not as bad as I think considering I am on a physics forum and there are probably a lot of WoW nerds, but now that I think about it, its worse than world or warcraft.

Edit: btw, I was going to put in homework section just cause it sounded like a homework question (and figuring people have more sympathy for a student and would respond quicker :p but it wouldn't let me start a topic. Search function would tell me but my phone is a pain so anyone care to tell a noob if its my phone messing up or is there a post count needed to use homework section?
 
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fellupahill said:
Long story. Not a homework question, tho sometimes I think the person running the contest would think to use a forum contest to do his coursework. But it's not.

Topic: Linear algebra.

If no one gets it right after 3 days then we can use any means to get the question right, now becomes a race.

Row reduce a 3x3 matrix A to the identity matrix.What is a basis for the matrix?
hint:
(Diagnose a 3x3 matrix over complex numbers and 2 of the complex eigenvalues are row reducing to identity matrices when you do A-lambda*I (where lambda is the eigenvalue

Not copied directly, doing on my phone so sorry for the terrible grammar. And I can't, well more like I don't want to, tell you the prize of the contest, its super nerdy and embarrassing. Maybe not as bad as I think considering I am on a physics forum and there are probably a lot of WoW nerds, but now that I think about it, its worse than world or warcraft.

Edit: btw, I was going to put in homework section just cause it sounded like a homework question (and figuring people have more sympathy for a student and would respond quicker :p but it wouldn't let me start a topic. Search function would tell me but my phone is a pain so anyone care to tell a noob if its my phone messing up or is there a post count needed to use homework section?

We generally do not allow contest-type questions on the PF, for the reason that you mention.

It does not take any post count to post in the Homework Help forums. However, contest-type questions are generally not allowed there either. Posters should fill out the Homework Help Template provided, including the Relevant Equations and Attempt at a Solution.
 

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