Can a 3x3 matrix have 4 eigenvalues?

  • Thread starter nicknaq
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  • #1
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Homework Statement



Prove or disprove the title of this thread.

Homework Equations


AX=(lamda)X


The Attempt at a Solution


I don't know where to start
 

Answers and Replies

  • #2
35,138
6,892

Homework Statement



Prove or disprove the title of this thread.

Homework Equations


AX=(lamda)X


The Attempt at a Solution


I don't know where to start

Start with the process you use to find the eigenvalues of a 3 x 3 matrix, which involves a determinant to get the characteristic equation for the matrix. What degree equation would you expect to get?
 
  • #3
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Start with the process you use to find the eigenvalues of a 3 x 3 matrix, which involves a determinant to get the characteristic equation for the matrix. What degree equation would you expect to get?

an equation of degree 3
 
  • #4
35,138
6,892
So it's not possible for a 3 x 3 matrix to have four eigenvalues, right?
 
  • #5
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So it's not possible for a 3 x 3 matrix to have four eigenvalues, right?

right. Is there any proof that I can say for why an equation of degree 3 cannot have 4 solutions?

I guess it's obvious though.
 
  • #6
214
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no its not possible. I had completed this topic only today in my class and here is one interesting question.

how to solve for eigen values. I think we need to take determinant. of A -[tex]\lambda[/tex] I

so we will get [tex]\lambda[/tex] cube in the equation which obviously will give three values of [tex]\lambda[/tex]
 

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