True/False: If true give a proof, if false give a counterexample.
If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X.
if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B
The Attempt at a Solution
2 0 2 3
0 2 has eigenvalue of 2; 3 2 has eigenvalue of 5
When I add them together (A+B) you get 4 3
Then I found an eigenvalue of 7; Is this correct?
Or the property of A+B != eigenvalueA + eigenvalueB is always correct? But this question's wording is kind of weird, because it said if its true give a counterexample ...
for a) I think it is false,...not entirely sure though.