Science:Math Exam Resources/Courses/MATH221/April 2013/Question 03
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Question 03 

There are two linear transformations of that map the square with vertices at to the square with vertices at . Call them and . Determine the matrices of and . 
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 

As the matrices must map the square edges to the square edges, we need to figure out where the four corners are mapped to. Use the fact that T_{1} and T_{2} are linear, which restricts your options. 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. As that matrices map the square to the square, it will map the corners to the corners, thus we will see all possible ways to map the four corners to the four new corners.
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