1. ## eigenvector

The matrix 1-2 25The matrix A = | 1 -2 |
| 2 5 |
has one eigenvalue of multiplicity 2. Find this eigenvalue and the corresponding eigenvector.

I know the eigenvalue is 3 but i am not sure how you find the eigen vector, any help is appreciated.

2. After you found the eigenvalue you must substitute the eignevalue into the formula:
(eigenvalueI-A)X=0
since the eigenvalue is 3 your matrix will look like:
2,2
-2,-2
carry this matrix to reduced row echelon form:
1,1
0,0
X is your eigenvector so the above matrix multiplied by X must equal 0. Say X is the column matrix = [a b] transposed. you get a=-b and b is arbitrary. Your eigenvector will then be:
-1
1