Thread: 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

Thanks in advance,
ArTiCk

Hi there

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]

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....

is eigenvector
and they are linearly dependent,....