I understand how to get eigenvalues, but I have a problem understanding eigenvectors.
I'll demonstrate with an example:
I am given A =
Solving for lambda, I get lambda = 1.5 and 4.5
Now my matrix equations become:
dividing by 1.5 I get:
so I get
Now, the answer is because if you set x1=1, then x2=1
If x1=x2, then why isn't the answer [ℝ ℝ], where ℝ is the set of all real numbers?