# Thread: Eigenvector problem

1. ## Eigenvector problem

I need to determine Eigen vectors for the following matrix

0 -1 4

3 1 -1

2 1 -2

When I place the lambdas on diagonal row and calculate the Det A - Lambda I

I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

Therefore the only eigenvalue I get is lamda = 1

Could someone please tell me if I am correct or not? Thanks Frostking

2. Hi there

Originally Posted by Frostking
I need to determine Eigen vectors for the following matrix

0 -1 4

3 1 -1

2 1 -2

When I place the lambdas on diagonal row and calculate the Det A - Lambda I

I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

Therefore the only eigenvalue I get is lamda = 1

Could someone please tell me if I am correct or not? Thanks Frostking

This is wrong, first of all I got another determinant.

And if you want to solve $\displaystyle \lambda^3 - \lambda^2 + 2 \lambda = 0$
then $\displaystyle \lambda = 0$

would be a solution too

I had -lambda^3 - lambda^2+6lambda = 0 instead of your solution

Hth
Rapha

3. Originally Posted by Frostking
I need to determine Eigen vectors for the following matrix

0 -1 4

3 1 -1

2 1 -2

When I place the lambdas on diagonal row and calculate the Det A - Lambda I

I am getting (-) lambda^3 - lamda^2 + 2 lamda = 0

Therefore the only eigenvalue I get is lamda = 1

Could someone please tell me if I am correct or not? Thanks Frostking
Your characteristic equation is wrong. The red 2 should be a 6.

There are 3 solutions. You should find them by first factorising the cubic.