- #1

LoopQG

- 22

- 0

## Homework Statement

Find the eigenvalues and eigenvectors of this matrix.

[4 0 1/2 ]

[0 -5 0 ]

[1/2 0 1 ]

**3. The Attempt at a Solution**

I have found the eigenvalues = -5, 5/2 + sqrt(5/2), 5/2 - sqrt(5/2)

I know to get the eigenvectors you subtract the eigenvalues from thediagonal and set each row equal to zero and solve for the 3 components.

for -5

[9 0 1/2]

[0 0 0]

[1/2 0 -5]

so 9x +1/2 z = 0

1/2x -5z=0

and y =0

but i get zero for all components even when i do the other eigenvalues. can anyone show me what i am doing wrong?

I have found the eigenvalues = -5, 5/2 + sqrt(5/2), 5/2 - sqrt(5/2)

I know to get the eigenvectors you subtract the eigenvalues from thediagonal and set each row equal to zero and solve for the 3 components.

for -5

[9 0 1/2]

[0 0 0]

[1/2 0 -5]

so 9x +1/2 z = 0

1/2x -5z=0

and y =0

but i get zero for all components even when i do the other eigenvalues. can anyone show me what i am doing wrong?