Science:Math Exam Resources/Courses/MATH307/December 2010/Question 01 (e)
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Question 01 (e) 

Let where a is a real number. (e) For what values of a (if any) is cond(A) = 4? 
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 

Part (d) suggests that some solutions for a exist. Find them by using the piecewise defined function mapping a to cond(A) found in Part (d). 
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. We use the three regions from part (d).
has the solutions a = 1/2, that is, a = 1/2 and a = 1/2.
has no solutions.
has the solutions a = 4 and a = 4. Overall we have that cond(A) = 4 holds if a = 4, a = 1/2, a = 1/2 or a = 4. 