Science:Math Exam Resources/Courses/MATH307/December 2005/Question 03 (f)
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Question 03 (f) 

Decide whether each of the following statements is true or false. You need not give a reason. All matrices in this question are square . If 2 is an eigenvalue of then 6 is an eigenvalue of 
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 

Start of with the associated eigenvector for the eigenvalue 2. Try applying the matrix to this vector. 
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. The statement is true. Let be the eigenvector of associated to the eigenvalue 2. Then
and so 6 is an eigenvalue for . 