- #1
ihumayun
- 12
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Homework Statement
The matrix A=
2 0 4
-2 0 -4
-1 0 -2
has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.
Eigenvalue =
Basis ( , , )T , ( , , )T
Homework Equations
The Attempt at a Solution
I have found the eigenvalue to be 0, but I can't seem to figure out how to come up with 2 bases. I found the first one:
2x + 4z = 0
-2x - 4z = 0
-1x - 1z = 0
All three equations reduce to :
x + 2z = 0
So then,
x = t , y = 0, and z = -(1/2)t
which gives a basis of (1, 0, -1/2)T
I'm not completely sure that I have calculated this correctly, and I have no idea how to come up with the second basis. The eigenvalue I calculated was marked correct, though. If anyone could help me, I would greatly appreciate it. :)