Find a basis for the eigenspace corresponding to the eigenvalue λ=2 of the matrix
A =
Hello,
Solve for in
This yields the following system :
(we can see that these two equations are actually the same).
There are two possibilities. Either y=1, either y=0.
If , then . For example, and
So is an eigenvector of the eigenspace.
If , then . For example, and
So is the second eigenvector of the eigenspace.
Does it look clear ?