Course 161/2S3, Tutorial, Trinity Term, April 2006
1. Write a C program to generate 6 lottery numbers, using the rand()
function. Your program should write numbers between 1 and 42 to an
array and should ensure that no numbers are repeated.
2. Consider the matrices


3 6 9


A =  2 5 −2  and B =
1 3 −1
4 1
1 5
!
(1)
.
Find the condition numbers κ(A) and κ(B) for the ∞ norm.
Recall that κ(A)∞ = ||A||∞ ||A−1 ||∞ and ||A||∞ = max1≤i≤n
ie. the maximum row sum.
Pn
j=1
|aij |,
Also recall that for 2 × 2 and 3 × 3 matrices the inverse matrix can be
determined by the following
A=
a b
c d
!
⇒ A
−1
1
=
detA
d −b
−c a
!
,
a13 a12
a33 a32
a12 a11 a32 a31 (3)
(2)
and


a11 a12 a13
1


A =  a21 a22 a23  ⇒ A−1 =
detA
a31 a32 a33
1
  


     

   a22 a23
a32 a33
a23 a21
a33 a31
a21 a22
a31 a32
a11 a13
a31 a33
a12 a13
a22 a23
a11 a12
a21 a22
a13 a11
a23 a21








.





