Finding Eigenvalues for a Matrix with One Real Eigenvalue of Multiplicity 2

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Discussion Overview

The discussion revolves around finding the value of \( k \) for which a given 2x2 matrix has one real eigenvalue of multiplicity 2. The focus is on the mathematical process of determining eigenvalues through the characteristic polynomial.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant presents the characteristic polynomial derived from the determinant, \( \mu^2 - 3\mu - 28 + 3k \), but expresses uncertainty about the next steps.
  • Another participant questions the correctness of the determinant computation, suggesting a need for reevaluation.
  • A later reply hints at using the quadratic formula after correcting the polynomial.
  • Another participant emphasizes the importance of considering the discriminant of the quadratic equation to determine the conditions for a double root.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correctness of the initial determinant computation, and multiple views on how to proceed remain evident.

Contextual Notes

There are unresolved steps regarding the computation of the determinant and the implications of the discriminant for the eigenvalue condition.

Who May Find This Useful

Students or individuals interested in linear algebra, particularly in the context of eigenvalues and characteristic polynomials.

jmcasall
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For which value of does the matrix
-4 k
-3 -7


have one real eigenvalue of multiplicity 2??

I use det(µI-A)=0
and end up with µ^2 - 3µ - 28 + 3k
but i don't know where to go from here
pls help
 
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think
 
haha thanks
 
jmcasall said:
For which value of does the matrix
-4 k
-3 -7


have one real eigenvalue of multiplicity 2??

I use det(µI-A)=0
and end up with µ^2 - 3µ - 28 + 3k
but i don't know where to go from here
pls help
you sure you computed the determinant correctly?

anyways after you correct it, hint: quadratic formula
 
yea you did do it wrong... do it again and then think
 
In particular, after you have the correct equation, think about the discriminant of the equation.
 
thanks
your help has been greatly appreciated
 

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