Science:Math Exam Resources/Courses/MATH307/December 2010/Question 01 (e)/Solution 1

We use the three regions from part (d).

• Case 1: If $0<|a|\leq 1$ then

$\displaystyle 4=\mathrm {cond} (A)=2/|a|$

has the solutions |a| = 1/2, that is, a = -1/2 and a = 1/2.

• Case 2: If $1\leq |a|\leq 2$ then

$\displaystyle 4=\mathrm {cond} (A)=2$

has no solutions.

• Case 3: If $2\leq |a|$ then

$\displaystyle 4=\mathrm {cond} (A)=|a|$

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.