Science:Math Exam Resources/Courses/MATH221/April 2013/Question 12 (c)
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Question 12 (c) 

Consider the plane x  y + z = 0. c) Find the 3x3 matrix P_{2} which represents projection of onto the given plane. 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Can you think of how to generalize what you did in part (b)? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We simply repeat the process we did in (b); for any vector u, we have that is in the plane. Thus, the projection onto the plane is given by the linear transformation , where I is the identity matrix. So, we compute it as follows: . 