Science:Math Exam Resources/Courses/MATH152/April 2012/Question 03 (b)
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Question 03 (b) 

Let A be the matrix for the linear transformation T. Suppose we know that , , are eigenvectors of A associated to the eigenvalues , , and respectively. Calculate . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Since A is the matrix for the linear transformation then 
Hint 2 

How can our knowledge from part(a) along with the fact that , , are eigenvectors help us? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The linear transformation acting on the vector will get given by From part (a) we have that In the question we are given the eigenvalues for these eigenvectors so we know Therefore 