Code: 1-MMN-525

Continuous assessment: Homework solutions and evaluation of the first set of tasks

solutions and evaluation of the second set of tasks

Final assessment:

86%-100% A

72%-86%   B

58%-72%   C

44%-58%   D

30%-44%   E

Exercise examples:

Exercise 1

Exercise 2

Exercise 3 solutions

Exercise 4 solutions

Exercise 5 

Procedure for decomposing a permutation into disjoint cycles for example 3c). The permutation can be represented using a directed graph, where arrows indicate how each number is mapped (see gif). We then untangle the resulting graph (see gif) and find that the permutation consists of two cycles, of lengths three and five, so a possible decomposition is (658)(13742). A cycle of length n consists of n-1 transpositions (swaps of two elements) and is even if n is odd, and odd if n is even. The parity of a permutation is the sum of the parities of all its disjoint cycles. In this case, both cycles are even, so the permutation is even.

Exercise 6 solutions

Exercise 7 solutions

Exercise 8 solutions

Completed homework from exercises 3, 4 and 8 can be sent together, i.e. all in one email, to the address rusin3(at)uniba.sk by the end of next week (3 May).

Exercise 9 solutions

Exercise 10 solutions

Exercise 11

Completed homework from exercises 9 and 10 can be sent together, i.e. all in one email, to the address rusin3(at)uniba.sk by the end of next week (24 May).

Literature:

Zlatoš, Pavol: Linear Algebra and Geometry: A Journey from Three Dimensions with Extensions to Related Fields, Bratislava, Albert Marenčin, 2011 
 Katriňák T., Gavalec M., Gedeonová E., Smítal J.: Algebra and Theoretical Arithmetic 1, ALFA Bratislava, 1985