# eigenvectors

• Nov 15th 2008, 03:38 PM
ArTiCK
eigenvectors
Hi all,

For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

First i found the eigenvalues by letting det(A- lamba*I) = 0....
the eigenvalue is lamda = 1

I then solve for my eigenvector

(A - I)v = 0

i row reduce (A - I) to [0 2; 0 0]

Now i am stuck... i don't know how to get my eigenvector

ArTiCk
• Nov 15th 2008, 06:24 PM
Rapha
Hi there

Quote:

Originally Posted by ArTiCK
Hi all,

For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

First i found the eigenvalues by letting det(A- lamba*I) = 0....
the eigenvalue is lamda = 1

I then solve for my eigenvector

(A - I)v = 0

i row reduce (A - I) to [0 2; 0 0]

$\displaystyle \begin{pmatrix} 0 & 2 \\ 0 & 0 \end{pmatrix}$

means, that you have to solve 2 equations

0*x+2*y = 0

0*x+2*y = 0

=> y = 0 and any x

x=1, x= 3 , x= - 10....

$\displaystyle \begin{pmatrix} x \\ 0 \end{pmatrix}$ is eigenvector
and they are linearly dependent,....