Science:Math Exam Resources/Courses/MATH221/April 2013/Question 07 (c)
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Question 07 (c) |
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Let be the linear transformation that reflects points through the line 3x = 4y. c) Compute A1995. |
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 |
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Consider what happens to a vector after successive reflections - it may help to write down a sample vector and it's first 3 or 4 reflections. Do you notice a pattern? |
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution 1 |
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Please rate my easiness! It's quick and helps everyone guide their studies. From the description of A, applying the matrix 1995 to is simply applying the same reflection 1995 times, but as reflections have order 2, i.e. applying it twice does nothing, and 1995 is an odd number, we see that . |
Solution 2 |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Alternatively, we can also show this by straightforward computation, using the breakdown in part b):
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