Contents
Exercise 1.

A college intends to install air-conditioning in three of its buildings during a one-week spring break. It invites three contractors to submit separate bids for the work involved in each of the three buildings. The bids it receives (in 1 000 dollar units) are listed in the following table:

BIDS
 Bldg Bldg Bldg 1 2 3 Contractor 1 47 87 41 Contractor 2 53 96 37 Contractor 3 60 92 36
Each contractor can install the air-conditioning for only one building during the one-week period, and so the college must assign a different contractor to each building. To which building should each contractor be assigned in order to minimize the sum of the corresponding bids? Use the Hungarian method.
Exercise 2.

 A = 1 2 0 3
 , B = - 1 2 3 4
 , C = 2 0 1 . 1 2 4

Find A + B,  4A - 2B,   AT,  BT,   CT,   (AT)T.

Exercise 3.

If A, B and C are as in the previous exercise, find out if a) C + CT is defined,   b) A + C is defined,   c)  A and B are symmetric. Show that AB BA.

Exercise 4.

 Let A = 1 , 2 0
 B = 1 3 , 2 0 0 1
 C = 2 1 0 . 0 1 -1 -1 0 2
Compute, if possible, a) CB,  ATB,  AB;         b)  BTCA,  BCA.
Exercise 5.

 Find all those matrices, which commute with the matrix 1 2 . 0 0

Exercise 6.

A zoo possesses birds(two-legged) and creatures(four-legged). If there are 300 heads and 1000 legs in the zoo, find out the number of birds and creatures.

Exercise 7.
Exercises 8-10
Contents
Index
All exercises