Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 03 (c)
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Question B 03 (c) 

Consider the matrix (c) Find a basis of eigenvectors of . 
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Hint 

If and be eigenvalue and eigenvector of a matrix (respectively), then we have 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From part (1), we have the corresponding eigenvector to as For the eigenvector corresponding to the eigenvalue , we solve Let now . Then, we have This means that and So, we have On the other hand, could be any real number. So, let to get
This means that and hence . Thus, putting for simplicity, we have Therefore, the basis of eigenvector of A is the set 
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Nobody voted on this yet Hard Easy 