Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (j)
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Question 12 (j) 

If v is an eigenvector of A, then v is also an eigenvector of 2A. 
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Hint 

Science:Math Exam Resources/Courses/MATH221/April 2009/Question 12 (j)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The answer is true. Suppose v is an eigenvector of A with corresponding eigenvalue . This means that . Then, multiplying by 2, we find . Hence v is also an eigenvector of 2A (corresponding to the eigenvalue ). 