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## Homework Statement

True/False: If true give a proof, if false give a counterexample.

a)

If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X.

b)

if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B

## Homework Equations

## The Attempt at a Solution

for b):

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

3 4

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.