- #1
JaysFan31
Homework Statement
I need to find the eigenvectors for the matrix shown below.
Homework Equations
Nothing relevant.
The Attempt at a Solution
I have the matrix
2 1 -1 0
0 4 -2 0
0 3 -1 0
0 3 -2 1
The eigenvectors are 1,1,2,2.
To get the eigenvectors for 1,1, I use the matrix
-1 1 -1 0
0 -3 -2 0
0 3 2 0
0 3 -2 0
When I bring this to RREF, I have
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 0
So I know that the vector
0
0
0
1
is an eigenvector.
But the book also says that
1
2
3
0
is an eigenvector for the eigenvalue 1.
If the matrix only has one solution, how do I get this other eigenvector?