SOLUTION: Hello I am having problems in solving the eigenvectors for the matrix: 3 0 8 -1 I have already calculated the eigenvalues which are -1 and 3 but I can not get the eigenvec

Algebra ->  Matrices-and-determiminant -> SOLUTION: Hello I am having problems in solving the eigenvectors for the matrix: 3 0 8 -1 I have already calculated the eigenvalues which are -1 and 3 but I can not get the eigenvec      Log On


   

Question 353075: Hello
I am having problems in solving the eigenvectors for the matrix:
3 0
8 -1
I have already calculated the eigenvalues which are -1 and 3 but I can not get the eigenvector, because of the zero in the top right hand corner.
Any help is much appreciated
Iman
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Don't let the zero throw you.
[A-cI]1=%28matrix%282%2C2%2C3-3%2C0%2C8%2C-1-3%29%29=%28matrix%282%2C2%2C0%2C0%2C8%2C-4%29%29
First eigenvector,c=3:
[A-cI]1[x]=
which leads to
0%2Ax%5B1%5D%2B0%2Ax%5B2%5D=0
8%2Ax%5B1%5D-4x%5B2%5D=0
which leads to
x%5B1%5D=1
x%5B2%5D=2
.
.
.
Second eigenvector,c=-1:
[A-cI]2=%28matrix%282%2C2%2C3%2B1%2C0%2C8%2C-1%2B1%29%29=%28matrix%282%2C2%2C4%2C0%2C8%2C0%29%29
[A-cI]2[x]=
which leads to
4%2Ax%5B1%5D%2B0%2Ax%5B2%5D=0
8%2Ax%5B1%5D%2B0%2Ax%5B2%5D=0
which leads to
x%5B1%5D=0
x%5B2%5D=1
.
.
.