# Can a 3x3 matrix have 4 eigenvalues?

## Homework Statement

Prove or disprove the title of this thread.

AX=(lamda)X

## The Attempt at a Solution

I don't know where to start

Mark44
Mentor

## Homework Statement

Prove or disprove the title of this thread.

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?

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

Mark44
Mentor
So it's not possible for a 3 x 3 matrix to have four eigenvalues, right?

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.

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 -$$\lambda$$ I

so we will get $$\lambda$$ cube in the equation which obviously will give three values of $$\lambda$$