Eigenvalues of the matrix are -1,-1,-2.

-1 with algebric multiplicity 2.

Eigenvectors for -1 are and

I am finding difficulty in getting eigenvectors for -2.

=

How to solve this.

I am getting z=0,y=0,and x=y-z.

Can anyone help me.

Printable View

- Nov 17th 2010, 07:08 AMkumaran5555problem in diagonalizing a matrix

Eigenvalues of the matrix are -1,-1,-2.

-1 with algebric multiplicity 2.

Eigenvectors for -1 are and

I am finding difficulty in getting eigenvectors for -2.

=

How to solve this.

I am getting z=0,y=0,and x=y-z.

Can anyone help me. - Nov 17th 2010, 07:25 AMFernandoRevilla
- Nov 17th 2010, 07:29 AMkumaran5555
I am just lost !!

- Nov 17th 2010, 08:41 AMHallsofIvy
You do NOT get y= 0.

is equivalent to the equations x- y+ z= 0, z= 0, and z= 0. That is, the last two equations are both z= 0.

With that, x- y+ 0= 0 so y= x. Any eigenvector is of the form <x, y, z>= <x, x, 0>= x<1, 1, 0>.