CS计算机代考程序代写 discrete mathematics The University of Melbourne — School of Mathematics and Statistics

The University of Melbourne — School of Mathematics and Statistics

MAST30012 Discrete Mathematics — Semester 2, 2021

Practise Class 11: Designs – Answers

Q1: Break the subsets into groupings of 3 lots of 4 subsets each. Each grouping is given to
a household and the detergents within the 4 subsets are compared over 4 days. The
detergents in the first subset are compared on day 1, those in the second subset on day 2
and so on.

As an extra feature the 4 subsets could be chosen so that all brands are included at least
once.

Q2: r = �


v � 1
k � 1


, r =

bk

v
; 3 6= 1⇥

8� 1
2� 1

= 7.

Q3: b = 10, v = 6, r = 5, k = 3,� = 2; 5 = 2⇥
6� 1
3� 1

; 5 =
10⇥ 3

6
.

Q4: Write down the incidence matrix and its complement by yourself.

The complement represents a design with parameters b = 10, v = 6, r = 5, k = 3,� = 2.

Q5: (a) Hint: Note that det(MTM) = det(MT )det(M) =

det(M)


2
.

(b) Hint: This follows from the definition of M .

(c) Hint: Use (b) and MTM = (k � �)I + �J .