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

  • Thread starter jmcasall
  • Start date
  • Tags
    Value
In summary, the question is asking for which value of k does the matrix have one real eigenvalue of multiplicity 2. The conversation discusses using det(µI-A)=0 and ending up with the equation µ^2 - 3µ - 28 + 3k, but not knowing where to go from there. A hint is given to use the quadratic formula and consider the discriminant of the equation to find the answer.
  • #1
jmcasall
5
0
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
 
Mathematics news on Phys.org
  • #2
think
 
  • #3
haha thanks
 
  • #4
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
 
  • #5
yea you did do it wrong... do it again and then think
 
  • #6
In particular, after you have the correct equation, think about the discriminant of the equation.
 
  • #7
thanks
your help has been greatly appreciated
 

1. What is an eigenvalue?

An eigenvalue is a scalar (single number) that is associated with a specific vector in a linear transformation. It represents the magnitude of the vector's stretch or compression in that transformation.

2. How is an eigenvalue calculated?

An eigenvalue is calculated by solving the characteristic equation of a matrix, which involves finding the roots of the equation det(A-λI) = 0, where A is the matrix and λ is the eigenvalue.

3. What is the significance of eigenvalues in linear algebra?

Eigenvalues are significant in linear algebra because they provide important information about the behavior of a matrix. They can determine whether a matrix is invertible, and they are used in many applications such as image processing and data analysis.

4. Can eigenvalues be complex numbers?

Yes, eigenvalues can be complex numbers. This means that the associated eigenvectors will also be complex. In some cases, complex eigenvalues can provide a more accurate representation of a linear transformation than real eigenvalues.

5. How are eigenvalues and eigenvectors related?

Eigenvalues and eigenvectors are related in that an eigenvalue represents the magnitude of the stretch or compression of an eigenvector in a linear transformation. Each eigenvector has a corresponding eigenvalue, and they are usually represented as a pair (λ, v) where λ is the eigenvalue and v is the eigenvector.

Similar threads

Replies
2
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
18
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
414
  • Introductory Physics Homework Help
Replies
8
Views
810
  • Calculus and Beyond Homework Help
Replies
2
Views
267
  • Introductory Physics Homework Help
Replies
6
Views
940
  • Set Theory, Logic, Probability, Statistics
Replies
0
Views
369
  • General Math
Replies
3
Views
816
  • Linear and Abstract Algebra
Replies
12
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
272
Back
Top