Science:Math Exam Resources/Courses/MATH221/December 2009/Question 04
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Question 04 

Link to the exam for the picture Let be the subspace of spanned by and where and Let T : be the reflection across W, find the standard matrix T. INSERT PICTURE HERE 
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Hint 

Science:Math Exam Resources/Courses/MATH221/December 2009/Question 04/Hint 1 
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Solution 

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A vector normal to the plain is given by which is To find the T matrix we need to find how the basis vectors are transformed. It is easy to see that gets transformed to itself because it lies on the plane. and are more difficult. For , imagine that we were looking directly on the x,z plane, the plane would then be squished into the line x = z. Then it is clear that the vector transforms into . Similarly, we can say that transforms into Hence, our transformation matrix is 