## elica85 3 years ago find eigenvector for eigenvalue -2...

1. elica85

after i plug in the value, i have the matrix |dw:1334524320293:dw|

2. elica85

multiplied 1st row by 2 and add to second row, multiply 1st row by -2 and add to 3rd row... |dw:1334524445998:dw|

3. elica85

multiply second row by -1/2 and add to 3rd row... |dw:1334524531744:dw|

4. elica85

so now i have these equations v1+v2+2v3=0 -2v2+2v3=0 -6v3=0

5. elica85

i'm not sure what the vector is, if v3=0, then -2v2+2(0)=0 so v2 must be 0 also and then v1+0+0=0 would mean v1 is zero too, right?

6. myko

but that's what you wanted |A-I(Lambda)| =0

7. myko

just put any value, for example v3=a and find the other

8. elica85

well for other eigenvalues, i have vectors with nonzero values...ok, if i plug in 3for v3, the last equation wouldn't make sense. and the answer isn't 0 vector. the vectors i have for my other values are correct

9. phi

you should get a singular matrix the last row should be 0

10. myko

-2v2+2a=0 v2=a v1+v2+2v3=0 v1+a+2a=0 v1 = -3a eigenvector (1,1,3)

11. elica85

it doesn't have to be all 0

12. myko

@phi is right the matrix should be singular. So you made a mistake somewhere

13. myko

|A-I(Lambda)| =0

14. phi

remember you are solving det(A- lambda*I)= 0

15. elica85

i was taught the bottom left triangle has to be 0s.

16. elica85

so it would be the bottom left corner, and the values right above and to the right

17. myko

the determinant has to be 0

18. elica85

i've checked and checked to see if i made a mistake...i will look again

19. phi

what is the original matrix?

20. myko

i think your eigenvalue is wrong

21. elica85

ugh idiot i did do it wrong. value is right, i will rework this

22. myko

just trying to help