Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 21
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Question A 21 

Consider the two perpendicular lines through the origin given below: Find the matrix for the composition of linear transformations: projection onto followed by projection onto . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Note that the lines are orthogonal. (graphing will help.) 
Hint 2 

The matrix of the linear transformation that projects on the straight line has the form: . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Give the formula in the hint, first we write the lines in the standard form . , . The matrix of projection onto is , and the matrix of projection onto is Thus projecting any point in 2D plane first on and then on can be represented by so the transformation matrix is In fact, since these two lines are orthogonal, projecting a vector (point) first on and then orthogonally projecting the new point on will return us to . 
Please rate how easy you found this problem:
Nobody voted on this yet Hard Easy 