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.

An example
Solution


Exercise 2.

A = 12
03
, B = - 12
34
, C = 201.
124

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

An example
Answer


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.

An example
Answer


Exercise 4.

Let A = 1,
2
0
B = 13,
20
01
C = 210.
01-1
-102
Compute, if possible, a) CB,  ATB,  AB;         b)  BTCA,  BCA.

An example
Answer


Exercise 5.

Find all those matrices, which commute with the matrix 12.
00

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Answer


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.

An example
Answer


Exercise 7.
Exercises 8-10
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