Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 05 (a)
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Question B 05 (a) 

Consider the matrix below:
It is known that is an eigenvalue of A. Find an eigenvector associated with the eigenvalue . 
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 

How do we solve for x with a given ? 
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 want to solve something of the form where I is the identity matrix. In this case we have so we have that
To solve (AI)x we write x=[a,b,c] and solve which is equivalent to solving This has solution b=c=a for any arbitrary a. Therefore we take a=1, without loss of generality, and our eigenvetor is
