Science:Math Exam Resources/Courses/MATH152/April 2013/Question B 04 (c)
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Question B 04 (c) 

Let A be the matrix given by It is known that is an eigenvalue of A. Find the other eigenvectors associated with and 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Compute the matrices and then check eigenvectors by inspecting the nullspace of this new matrix, for each value of . It will simplify matter when you use vectors with the middle entry equal to 0. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We compute the matrices and check its nullspace and from this we can see that is an eigenvector associated to (to get all eigenvectors, multiply this vector by any nonzero number). Repeating this with and from this we can see that is an eigenvector associated to (to get all eigenvectors, multiply this vector by any nonzero number). 