Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 06 (a)
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Question B 06 (a) 

The matrix A below represents a transformation that reflects vectors in in a plane that contains the origin. Note: you can use geometric insight to greatly simplify the calculations below. (a) Find all eigenvalues and a basis of eigenvectors of 
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Hint 

Since is a reflection matrix, its eigenvalues are only. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. When . We need to find such that Thus and are solutions. By normalizing, we have and
Thus, the eigenvalues and eigenvector basis are 
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