MATH307 December 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q6 (f) • Q7 (a) • Q7 (b) • Q7 (c) •
Question 01 (e)
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!
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).
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We use the three regions from part (d).
- Case 1: If then
has the solutions |a| = 1/2, that is, a = -1/2 and a = 1/2.
- Case 2: If then
has no solutions.
- Case 3: If then
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.
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