Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 21
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Question A 21 

find values and such that . Note: one set of such values is sufficient. 
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 

Note that a matrix satisfies is an orthogonal matrix. 
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. Following the hint, we know that is an orthogonal matrix. That is, the two column vectors are orthogonal to each other and have norms of . The orthogonal condition implies that and the norm condition implies By solving these equations, we get a solution: . 