## 7 Discussion  
Obtaining optimal performance parameters of the spraying nozzles used in agricultural sprayers is conditioned by many factors of operational nature. These factors have a significant impact on the effectiveness of the pesticides used [36]. In the construction of an agricultural sprayer, it is the spraying nozzle that determines the quality of the obtained sprayed liquid stream. In the countries where mandatory sprayer inspection has been adopted, various methods are used to determine the degree of wear of sprayer nozzles. Methods of measuring the outflow rate and methods of measuring the fall of the sprayed liquid are used [37]. A method of testing single nozzles was also proposed, and the results obtained from single nozzles are used to build a virtual boom of a field sprayer [38; 39]. The results of the transverse distribution of the sprayed liquid obtained from single nozzles can be combined in any way to obtain a satisfactory distribution coefficient for the entire field sprayer boom. Currently, there are many computing applications for simulating the assumed operating parameters [40; 41]. The quality of spray nozzle operation has a significant impact on spraying efficiency as well as the spectrum of droplets formed. Worn-out nozzles may produce droplets of different size classes than their equivalents in new nozzles [42]. The size of the produced droplets has a significant impact on their susceptibility to drift, which has a significant impact on the safety of the environment and the area surrounding the sites of plant protection treatments [43; 44; 45]. This parameter may also determine the effectiveness of treatment performance [46; 47]. According to the authors' knowledge, the first paper that attempts to optimise the sequence and orientation of the nozzles used on the sprayer beam dates to 2005 [48]. The authors of this paper employ sparse matrices, i.e., such matrices that typically contain only zeros except for block submatrices, which have only ones on the diagonals. Thereby, they attempt to describe the phenomenon of the permutation of nozzles on a linear beam with the possibility of changing their orientation by applying instruments of linear algebra. Unfortunately, this paper demonstrates the authors' limited experience and mathematical imagination. The paper contains a multitude of factual errors, leading to a departure from the problem formulated in the paper. Hence, according to Figure 1 of the paper quoted here, because there are five submatrices which \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Groups of Nozzles**} & \multicolumn{3}{c}{**Value of the Coefficient of Variation [\%]**} & \multicolumn{1}{c}{**Spread**} & \multicolumn{1}{c}{**Quotient [\%] of the**} & \multicolumn{1}{c}{**The Quotient [\%]: of**} \\  & **Initial** & **Maximum** & **Minimum** & **Points]** & **Maximum Value and** & **the Spread and the** \\ \hline \multirow{2}{*}{Old} & A & 20.7\% & **25.4\%** & 13.0\% & **12.4** & **195.7\%** & **95.7\%** \\  & B & 16.3\% & **20.6\%** & 11.1\% & **9.4** & **184.7\%** & **84.7\%** \\ \hline \multirow{2}{*}{New} & C & **9.0\%** & **11.5\%** & 7.5\% & **4.0** & **152.5\%** & **52.5\%** \\  & D & **8.6\%** & **10.4\%** & **6.5\%** & **3.9** & **160.2\%** & **60.2\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The value of the coefficient of variation [%] for groups A–D on tables with 0.1 m wide grooves, depending on the sequencing and method of mounting flat fan nozzles on the boom of a field sprayer. are not of full column rank the permutation of these submatrices of matrix A, which is presented there, does not correspond to a permutation of the nozzles but to a replacement by other nozzles that the authors will not have at their disposal. The situation is similar with the attempt at changing orientation. On the other hand, according to Figure 4 of the paper quoted here, there are five submatrices, all of which are already of full column rank, and these present five types of nozzles, three identical ones for each type.