Exercise 1

Calculate the sum of matrices kA+mB if

The elements of the sum matrix are determined by the formula:

cij=kaij+mbij.

Calculate the elements of the first row of the sum matrix:

C11=-4*2+5*3=7

C12=-4 * (-1)+5 * 7=39

C13=-4*4+5*(-2)=-26

C21=-4*6+5*9=21

C22=-4*3+5*1=-7

C23=-4*0+5*6=30

С31=-4 * (-7)+5 * (-4)=8

C32=-4*5+5*8=20

C33=-4*9+5*5=-11

Thus, the sum matrix will take the form:

Task 2

Calculate the inverse matrix and check.

We use the algorithm for finding the inverse matrix:

• 1. The matrix is ​​​​square (the number of rows is equal to the number of columns), therefore, the matrix inverse to it exists.
• 2. Find the determinant of the original matrix:

• ?A=-3 * 3 * 3+1 * (-5) * 1+0 * (-4) * 3-1 * 3 * 3-(-4) * 1 * 3-0 * (-5) * (-3)=-29 ? 0
• 3. Find a matrix consisting of algebraic complements of elements of the original matrix:

A11=(-1) 2*3*3-0*(-5)=-9

A12=(-1) 3 * -4 * 3-1 * (-5)=7

A13=(-1) 4 * -4 * 0-1 * 3=-3

A21=(-1) 3*1*3-0*3=-3

A22=(-1) 4*-3*3-1*3=-12

A23=(-1) 5 * -3 * 0-1 * 1=1

A31=(-1) 4*1*(-5)-3*3=-14

A32=(-1) 5 * -3 * (-5)-(-4) * 3=-27

A33=(-1) 6 * -3 * 3-(-4) * 1=-5

Thus, we get the matrix:

4. Transpose the resulting matrix:

5. We divide the last matrix by the determinant of the original matrix and get the inverse matrix:

6. We check the result. To do this, we find the product of the resulting matrix by the original one:

A -1 .* A=A * A -1 =*= ==

Thus, we got the identity matrix as a result. Consequently, inverse matrix found, right.

Task 3

Solve the system linear equations Cramer, Gauss method.

Solution:

1) Solve the system by Cramer's method.

We compose the matrix of the system:

We calculate the determinant of this matrix:

0 * (-8) * 4+3 * 2 * (-5)+7 * 2 * 9-9 * (-8) * (-5)-3 * 7 * 4-0 * 2 * 2=-348?0

Finding determinants? 1 , ?2, ?3, obtained from the original determinant by replacing the first, second and third columns, respectively, with a column of free members:

1==2 * (-8) * 4+3 * 2 * (-3)+9 * 5 * 2-9 * (-8) * (-3)-3 * 5 * 4-2 * 2 * 2=-276

2==0 * 5 * 4+2 * 2 * (-5)+9 * 7 * (-3)-9 * 5 * (-5)-2 * 7 * 2-0 * 2 * (-3)=- 40

3==0 * (-8) * (-3)+3 * 5 * (-5)+2 * 7 * 2-2 * (-8) * (-5)-3 * 7 * (-3)-0 * 5 * 2=- 64

Now using Cramer's formulas

x1=, x2=, x3= ,

find the solution of the system:

X1==,=0.79 x2==,=0.11 x3===0.18

2) We solve the system using the Gauss method.

We compose the extended matrix of the system, which includes coefficients for variables and free terms:

Multiply the 2nd row by (5). Multiply the 3rd row by (7). Let's add the 3rd line to the 2nd:

Multiply the 1st row by (26). Multiply the 2nd row by (3). Let's add the 2nd line to the 1st:

From the 1st line we express x 3

From the 2nd line we express x 2

26x 2 \u003d - + 4 \u003d 0.11

From the 3rd line we express x 1

5x 1 \u003d -2 * 0.11- - 3 \u003d 0.79

Task 4

matrix determinant linear Cramer gauss

Calculate the 4th order determinant

We write the expansion of the determinant in the fourth line:

A \u003d\u003d 0 * A 41 +3 * A 42 +0 * A 43 +1 * A 44

where Aij is the algebraic complement of the element ij a .

Let's find algebraic additions according to the formula A ij =(-1) i+j , where m ij is the minor of the element ij a, which is obtained from the original determinant by deleting the row and column at the intersection of which this element stands.

A 42 \u003d (-1) 4 + 2 * m 42 \u003d (-1) 6 * \u003d 4 * 7 * (-9) + 7 * (-7) * 0 + 1 * (-1) * 0 - 0 * 7 * 0 - 7 * 1 * (-9) - 4 * (-7) * (-1) = -217

A 44 \u003d (-1) 4 + 4 * m 44 \u003d (-1) 8 * \u003d 4 * (-3) * (-1) + 0 * 7 * 0 + 1 * 1 * 7-7 * (-3 ) * 0-0 * 1 * (-1)-4 * 7 * 1=-9

We substitute the obtained values ​​into the expansion of the determinant:

3 * A 42 + A 44 \u003d 3 * (-217) + (-9) \u003d -660

Task 5

inverse determinant matrix linear Cramer gauss

Independently, by analogy with the example, create a problem with economic content, build mathematical model economic process, and solve the problem.

A task.

The costs of three types of raw materials A, B, C for the production of a unit of each of the three types of products I, II, III and the reserves of each type of raw material are given in the table (Table 1):

Table 1

Products Type of raw material				Stocks of raw materials

It is required to determine a production plan that ensures the use of all raw materials.

Let's write a system of linear equations using the data given in the table:

where - the volume of output of each type.

To solve, we use the Gauss method. Let's write the augmented matrix of the system:

We write the system in the form of an extended matrix:

Multiply the 2nd row by (-2). Let's add the 2nd line to the 1st:

Multiply the 2nd row by (3). Multiply the 3rd row by (-1). Let's add the 3rd line to the 2nd:

Multiply the 1st row by (2). Let's add the 2nd line to the 1st:

Now the original system can be written as:

x2 = /2

x 1 = /3

From the 1st line we express x 3

From the 2nd line we express x 2

From the 3rd line we express x 1

It makes it possible to determine the optimal sequence for studying the subjects included in the curriculum. Each subject in the curriculum has its own number.

Let the curriculum include 19 subjects. We build a square matrix with a base, which is equal to the number of subjects in the curriculum (19).

The method of expert assessment by experienced teachers determines the most significant relationships between academic subjects. The columns of the matrix are considered consumers, and the rows are considered information carriers. For example, for column 10, lines 7, 9, 11 are important information carriers, that is, knowledge on subjects with these numbers. These rows in the column are reflected by ones (1), the absence of a cash connection - by zeros (0). As a result of the analysis, a matrix of the nineteenth order was formed. The analysis of the matrix consists in the sequential removal of columns and rows. Columns filled with zeros do not receive information from other subjects, that is, their study is not based on a logical relationship with other subjects, although they, in turn, can be carriers of primary information. This means that subjects that have numbers in these columns can be studied first. Lines filled with zeros are not considered information carriers and will not be the basis for studying other subjects, which means they can be studied last.

First, columns 7,8, 9,18 and their corresponding rows are crossed out. We get the first reduced matrix of the fifteenth order, which in turn has zero columns 4, 16, 17. Getting rid of them, we get the second reduced matrix. Having thus carried out all subsequent reductions, we obtain a matrix in which there are no columns without ones, but there are zero rows, which are also crossed out along with their corresponding columns. Having successively performed similar actions, we arrive at a matrix of this form, as shown in the diagram.

The formed matrix corresponds to the graph shown in Figure 3.2. This graph contains three closed double contours (13-15), (5-6), (11-10). With some approximation, we can assume that the subjects that entered these circuits should be studied in parallel, and first subjects with numbers 13 and 15 are studied, and only then subjects 5, 6, 10, 11.

As a result of the conducted matrix analysis, it becomes possible to create a schematic (block) model of the study of subjects in the curriculum:

The diagram shows a combined system for connecting educational subjects. The cells contain the numbers of subjects with parallel study. An educated connection system should be understood not as a mandatory sequence of connecting one group of subjects only after the end of the previous one, but only as a need to get ahead in their study. It only indicates a general trend in the connection of objects.

Matrix Analysis Program

Allows you to evaluate the logical sequence of the location educational material within the subject and improve it accordingly.

Let the subject include 6 topics. Matrix A! compiled according to the thematic plan of this academic subject. The numbers of topics that, when compiling the matrix, are considered in terms of their use in the study of other topics are arranged vertically, the numbers located horizontally correspond to the topics considered in terms of their use of information from other topics.

To identify closed loops, the presence of which indicates the impossibility of establishing the passage of the sequence of passage of individual topics, we carry out transformations (shortening) of the matrix Au. We delete row 5, consisting of zeros, and the column corresponding to it, as well as the zero column 3 with the corresponding row. Matrix A2 is formed.

The matrix A2 has missing rows and columns consisting of only zeros. To establish closed contours, we present the graph corresponding to the matrix A2 (see Fig. 3.3, a).

From the study of the graph, it follows that the presence of closed contours is caused by the relationship between the content of the educational material of topics 1 and 6, as well as topics 4 and 6. The reason for the noted relationship is the unsuccessful redistribution of the content of the educational material between these topics. By reviewing the content of these topics, it becomes possible to eliminate existing closed loops graph. Thus, a new graph is formed (Fig. 3.3, b) and the corresponding matrix A3.

Reducing this matrix gives a new matrix A4.

After removing the arcs (6, 4), (6, 1) and (1, 6), we obtain a new initial matrix B1, the graph of which has no closed contours.

Now that the loops are broken, let's start adjusting the order of the topics. To do this, we will sequentially delete columns consisting of zeros and rows of the same name with them. Topics in these columns do not use information from other topics and can therefore be explored first.

In the matrix! columns 1 and 3 are null. Thus, topic 1 can take its place in the thematic plan. When examining the reasons for putting Topic 3 before Topic 2, it turns out that some of the information on Topic 2 takes place in Topic 3. However, it is more logical and more useful to leave them in Topic 3.

After rearranging the educational material, instead of the arc (3, 2) we get the arc (2, 3); delete column 1 - we get the matrix B2.

We assign the former number 2 to topic 2. Delete column 2 row 2. We get matrix B3.

Themes 3 and 4 remain with the same numbers. Delete columns 3, 4 with the corresponding rows; we get the matrix B4

Topic 6 is assigned number 5, and topic 5 is number 6.

We compose matrix C1 according to the new distribution of topics.

Let's carry out transformations of the matrix, sequentially deleting zero rows and columns with the same name. We move the topics corresponding to them to the end of the row, because the information of these topics is not used in the study of other topics. Topic 5 is assigned the number 6.

Delete row and column 6. Assign topic 6 number 5.

We delete lines 4 and 3 and assign the topics that they answer to former numbers 4 and 3.

For topics 1 and 2, the same numbers remain in the thematic plan. As a result of the matrix processing, the following final arrangement of topics in the structure of the subject is obtained:

It can be seen from the above sequence that after matrix processing of the structure thematic plan topics 5 and 6 have swapped places. In addition, it became necessary to move the educational material on topic 5 to topic 1, as well as from topic 2 to topic 3.

As can be seen from the above example, the matrix analysis of the structure of the educational material makes it possible, to a certain extent, to streamline it and improve the mutual arrangement of the topics of the curriculum.

It should be taken into account that the matrix analysis of curricula and programs requires the performers to have a lot of practical experience and a deep knowledge of the content of the training. First of all, this refers to the compilation of the initial matrix, more precisely, to the definition of links between academic subjects or learning topics inside the subject. There are many connections between such large elements as program topics, but matrix analysis performers must be able to "read between the lines" (find hidden but real connections), determine the significance of various connections in relation to the goals of matrix analysis, and sometimes be critical of the content of the topics of educational subjects.

Matrix analysis or the matrix method has become widespread in the comparative evaluation of various economic systems (enterprises, individual divisions of enterprises, etc.). The matrix method allows you to determine the integral assessment of each enterprise for several indicators. This assessment is called the rating of the enterprise. Consider the application of the matrix method in stages using a specific example.

1. Selection of evaluation indicators and formation of a matrix of initial data a ij, that is, tables, where the numbers of systems (enterprises) are reflected in rows, and the numbers of indicators (i = 1,2 ... .n) - systems are reflected in columns; (j=1,2…..n) - indicators. The selected indicators should have the same focus (the more, the better).

2. Compilation of a matrix of standardized coefficients. In each column, the maximum element is determined, and then all elements of this column are divided by the maximum element. Based on the results of the calculation, a matrix of standardized coefficients is created.

We select the maximum element in each column.

In strategic planning and marketing, quite a lot of matrices of one direction or another are used. There is a need to systematize these matrices, as well as to gradually introduce the matrix approach at all stages of strategic analysis and planning.

Levels of strategic planning in the matrix dimension. In strategic planning, one can single out the corporate level, the business level, and the functional level.

Strategic planning matrices at the corporate level analyze the businesses included in the corporation, i.e. help to carry out portfolio analysis, as well as analysis of the situation in the corporation as a whole.

The business layer includes matrices that are relevant to a given business unit. Matrices and refer most often to one product, analyze the properties of this product, the situation on the market for this product, etc.

Functional level matrices explore the factors that affect the functional areas of the enterprise, of which the most important are marketing, personnel.

Classification of matrices of strategic analysis and planning.

Existing strategic analysis and planning matrices explore various aspects of this process. The classification of matrices is necessary to identify patterns and features of the application of the matrix method in strategic analysis and planning.

Matrices according to existing features can be classified as follows:

• Classification by the number of cells under study.

The more cells the matrix contains, the more complex and informative it is. In this case, it is possible to divide the matrices into four groups. The first group includes matrices consisting of four cells. In the second group there are matrices consisting of nine cells, in the third - from sixteen, in the fourth - more than sixteen cells.

• Classification by object of study.

Classification according to the object of study divides the matrices into groups depending on the object under study. In the Awareness-Attitude matrix, the object of study is the staff, as well as in the matrix “The impact of pay on group relationships”. Another object of study is the portfolio of the company. Shell/DPM, BCG matrices can serve as examples in this group.

• Classification according to the information received.

This classification divides the matrices into two groups according to the information received: either quantitative or semantic. In this group, an example of a matrix formed due to information in the form of a number is the matrix of the vector of the economic state of the organization, and formed due to logical information - a matrix of the main forms of associations.

The introduction of matrix tools in the analysis and planning of the enterprise.

At the first stage, it is proposed to make a primary analysis of the enterprise. Three matrices have been selected for this purpose. The SWOT matrix is ​​widely described in the literature. The MCC matrix involves an analysis of the compliance with the mission of the enterprise and its main capabilities. vector matrix economic development enterprise is a table that presents the numerical data of the main indicators of the enterprise. From this matrix, you can draw information for other matrices, as well as draw various conclusions based on these data already at this stage.

The second step in the application of matrix methods is the analysis of the market and industry. It analyzes the markets in which the company operates, as well as the industry as a whole. The main ones in the “Market” subgroup are the BCG matrix, which examines the dependence of growth rates and market share, and the GE matrix, which analyzes the comparative attractiveness of the market and competitiveness in the industry and has two varieties: the Daya variant and the Monienson variant. The "Industry" subgroup contains matrices that study the industry environment, patterns of industry development. The main one in this subgroup is the Shell/DPM matrix, which examines the relationship between industry attractiveness and competitiveness.

The next steps in strategic planning are differentiation analysis and quality analysis. Differentiation and quality are in this case as components with the help of which it is possible to obtain the desired result. There are three matrices in the "Differentiation" group. The matrix "Improving the competitive position" allows you to visually identify patterns and dependencies of differentiation on market coverage. The "Differentiation - Relative Cost Effectiveness" matrix reveals the relationship between relative cost effectiveness in a given market and differentiation. The Performance-Innovation/Differentiation matrix shows the relationship between the performance of a given business unit and the adoption of innovations.

The object of study of the "Quality Analysis" group is the identification of factors and patterns that affect such an aspect as the quality of products. A group can include two matrices. The Pricing Strategies matrix positions products based on quality and price. The matrix "Quality - resource intensity" determines the ratio of the quality of the product produced and the resources spent on it.

The "Management Analysis" and "Marketing Strategy Analysis" groups are not included in the step-by-step implementation of the matrix method in strategic planning. These groups are isolated. The matrices that make up these groups can be applied at all stages of strategic planning and address issues of functional planning. The Control Analysis group consists of two subgroups. The first subgroup - "Management" - considers the management of the company as a whole, the processes that affect the management, management of the company. The subgroup "Personnel" considers the processes taking place between colleagues, the influence of various factors on the performance of staff.

In the proposed scheme of strategic analysis and planning in each group, the matrices interact with each other, but one cannot rely on the result or conclusion of only one matrix - it is necessary to take into account the conclusions obtained from each matrix in the group. After the analysis in the first group, the analysis in the next one is carried out. Analysis in the "Management" and "Marketing Strategy" groups is carried out at all stages of the analysis in strategic planning.

Characterization of individual matrices

SWOT analysis is one of the most common types of analysis in strategic management today. SWOT: Strengths (Forces); Weaknesses (Weaknesses); Opportunities (Opportunities); Threats. SWOT analysis allows you to identify, structure the strengths and weaknesses of the company, as well as potential opportunities and threats. This is achieved by comparing the internal strengths and weaknesses of their company with the opportunities that the market gives them. Based on the quality of compliance, a conclusion is made about the direction in which the business should develop, and ultimately the distribution of resources by segments is determined.

The purpose of the SWOT analysis is to formulate the main directions for the development of the enterprise through the systematization of the available information about the strengths and weaknesses of the company, as well as potential opportunities and threats.

The most attractive thing about this method is that the information field is formed directly by the leaders themselves, as well as by the most competent employees of the company, based on the generalization and coordination of their own experience and vision of the situation. A general view of the matrix of the primary SWOT analysis is shown in Fig.1.

Fig.1. Matrix of primary strategic SWOT - analysis.

Based on a consistent consideration of factors, decisions are made to adjust the goals and strategies of the enterprise (corporate, product, resource, functional, managerial), which, in turn, determine the key points of organizing activities.

Analysis of a company's business portfolio should help managers evaluate the company's field of activity. The company should strive to invest in more profitable areas of its activities and reduce unprofitable ones. The first step of the management in the analysis of the business portfolio is to identify the key areas of activity that define the mission of the company. They can be called strategic elements of business - SEB.

In the next step of the business portfolio analysis, management must assess the attractiveness of the various SEBs and decide how much support each of them deserves. In some companies, this happens informally during the course of work. Management examines the totality of the company's activities and products and, guided by common sense, decides how much each SEB should bring and receive. Other companies use formal methods for portfolio planning.

Formal methods can be called more precise and thorough. Among the most well-known and successful methods of business portfolio analysis using formal methods are the following:

• Boston Consulting Group (BCG) method;
• General Electric (GE) method.

The BCG method is based on the principle of analysis of the growth/market share matrix. This is a portfolio planning method that evaluates a company's SEB in terms of their market growth rate and the relative market share of those items. SEBs are divided into "stars", "cash cows", "dark horses" and "dogs" (see Fig. 2).

T e m P R about With t a R s n to a	in s With about to and th	"Star"	"Cash cows"
	n and h to and th	"Milch cow"	"Dog"
		high	low
Relative market share

Fig.2. BCG Matrix.

The vertical axis in Figure 2, the market growth rate, determines the measure of market attractiveness. The horizontal axis, relative market share, determines the strength of a company's position in the market. When dividing the growth/market share matrix into sectors, four types of SEBs can be distinguished.

"Stars". Rapidly developing lines of business, products with a large market share. They usually require heavy investment to sustain their growth. Over time, their growth slows down, and they turn into "cash cows".

"Cash Cows". Lines of business or products with low growth rates and a large market share. These sustainable, successful SEBs require less investment to maintain their market share. At the same time, they bring in high income, which the company uses to pay its bills and to support other SEBs that require investment.

"Dark Horses" Business elements with a small share of high-growth markets. They demand a large number funds even to maintain its market share, let alone increase it. Management should carefully consider which "dark horses" should be turned into "stars" and which should be phased out.

"Dogs". Lines of business and products with low growth rate and small market share. They may generate enough income to support themselves, but do not promise to become more serious sources of income.

Each SEB is placed on this matrix in proportion to its share in the company's gross income. After classifying the SES, the company must determine the role of each element in the future. For each SEB, one of four strategies can be applied. A company may increase investment in an element of the business in order to gain market share for it. Or it can invest just enough to keep the SEB share at the current level. It can drain resources from the SEB by withdrawing its short-term monetary resources over a certain period of time, regardless of long-term consequences. Finally, it can deinvest in the SEB by selling it or going into a phase-out and use the resources elsewhere.

Over time, the SEB changes its position in the growth/market share matrix. Each SEB has its own life cycle. Many SEBs start as "dark horses" and, under favorable circumstances, move into the category of "stars". Later, as the market slows down, they become "cash cows" and, finally, at the end of their life cycle fade away or turn into "dogs". Companies need to continuously introduce new products and activities so that some of them become "stars" and then "cash cows" that help finance other SEBs.

Matrix methods play a very important role in strategic analysis, planning and marketing. The matrix method is very convenient - this explains its prevalence. However, the use of only matrix methods is not sufficient, since matrices allow you to explore strategic planning and marketing from separate angles, and do not show the full picture, but in combination with other methods, the matrix approach makes it possible to visually see the patterns in the processes taking place in the enterprise and make correct conclusions.

Table 1. Matrix tools in the analysis and planning of the organization's activities

№	Levels of problem solving	Matrix	Main characteristics
1	Primary Analysis	SWOT matrix	Analysis of the strengths and weaknesses of the enterprise, opportunities and threats
2		Matrix MCC	Analysis of compliance with the mission of the enterprise and its main capabilities
3		Matrix of the vector of economic development of the enterprise	Analysis of statistical data
4	Market/industry analysis	BCG Matrix	Analysis of growth rates and market share
5		Matrix GE	Analysis of comparative market attractiveness and competitiveness
6		ADL Matrix	Industry life cycle analysis and relative market position
7		Matrix HoferSchendel	Analysis of the position among competitors in the industry and the stage of market development
8		Ansoff matrix (“market-product”)	Analysis of strategy in relation to markets and products
9		Porter matrix (five competitive forces)	Analysis of strategic prospects for business development
10		Elasticity matrix of competitive response in the market	Analysis of the company's action on the factors of competitiveness of the product, depending on the elasticity of the reaction of the priority competitor for the product
11		Product grouping matrix	Product grouping analysis
12		Matrix “Impact Uncertainty”	Analysis of the level of impact and degree of uncertainty when entering a new market
13	Industry	Cooper matrix	Analysis of industry attractiveness and business strength
14		ShellDPM Matrix	Analysis of the attractiveness of a resource-intensive industry depending on competitiveness
15		Downturn Strategies Matrix	Analysis of competitive advantages in the industry environment
16		Matrix of basic join forms	Analysis of association in an industry environment
17	Analysis of differentiation	Competitive Position Improvement Matrix	Analysis of differentiation and market coverage
18		Matrix “Differentiation Relative Cost Effectiveness”	Analysis of differentiation and relative cost effectiveness
19		Matrix “Performance - Innovation/Differentiation”	Analysis of innovation/differentiation and performance
20	Quality analysis	Matrix “Price-quality”	Product positioning depending on quality and price
21		Matrix “Quality-resource intensity”	Analysis of the dependence of quality on resource intensity
22	Marketing strategy analysis	Brand Family Extension Strategy Matrix	Analysis of the dependence of distinctive advantages and segmentation of the target market
23		Matrix “Awareness - attitude to the brand of goods”	Analysis of the relationship between gross profit margin and sales response
24		Marketing Channel Matrix	Analysis of the relationship between the pace of market development and the value added by the channel
25		Matrix “Contact- service adaptation level”	Analysis of the dependence of the level of adaptation of services to the requirements of clients on the degree of contact with the client
26		Matrix “Marketing Diagnostics”	Analysis of the dependence of the strategy on the implementation of the strategy
27	Management Analysis Management	Matrix of strategic management methods	Analysis of the dependence of strategy and the impact of planning
28		Matrix of the strategic management model	Analysis of the dependence of the management model on the type of changes
29		Hersey-Blanchard matrix	Analysis of the situational leadership model
30		Ohio University Leadership Style Dimension Combinations Matrix	Analysis of Combinations of Leadership Style Dimensions
31		Matrix “Management Grid”	Leadership type analysis
32	Staff	Matrix "Change - in the organization"	Analysis of the dependence of changes occurring in the organization and resistance to these changes
33		Matrix of the influence of payment on relationships in the group	Analysis of the dependence of relationships in the group on the differentiation of payment
34		Matrix of types of inclusion of a person in a group	Analysis of the relationship between the attitude to the values ​​of the organization and the attitude to the norms of behavior in the organization
35		Matrix “Key Business Capabilities”	Analysis of the market and key business capabilities
36		Matrix “Importance of work”	Analysis of the dependence of the performance of work on the importance
37		Matrix of existing formal systems of performance criteria	Analysis of existing formal systems of performance criteria
38		Performance management results matrix	Analysis of the results of management of performance criteria
39		Blake-Mouton matrix	Analysis of the dependence of the performance of work on the number of people and on the number of tasks
40		McDonald Matrix	Performance analysis

method scientific research properties of objects based on the use of the rules of the theory of matrices, which determine the value of the elements of the model, reflecting the relationship of economic objects. It is used in cases where the main object of study is the balance ratio of costs and results of production and economic activities and the standards of costs and outputs.

• - pseudobridge, matrix bridge

  Molecular biology and genetics. Dictionary

• - English. matrix analysis; German Matrixanalysis. In sociology - a method of studying the properties of social. objects based on the use of the rules of matrix theory...

  Encyclopedia of Sociology

• - in the printing industry - a press for embossing stereotypical matrices or non-metal. stereotypes are usually hydraulic...

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• - A device used for pressing cardboard or vinyl plastic matrices, as well as plastic stereotypes ...

  Brief explanatory dictionary of polygraphy

• - See: dot matrix printer...

  Glossary of business terms

• - a method of scientific study of the properties of objects based on the use of the rules of the theory of matrices, which determine the value of the elements of the model, reflecting the relationship of economic objects ...

  Big Economic Dictionary

• - in economics, a method of scientific study of the properties of objects based on the use of the rules of the theory of matrices, which determine the value of the elements of the model, reflecting the relationship of economic objects ...

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• - a method for studying the relationships between economic objects using their matrix modeling ...

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Matrix metering

From the book Digital Photography from A to Z author Gazarov Artur Yurievich

Matrix metering Matrix metering (Pattern Evaluative, E) is also called multi-zone, multi-zone, multi-segment, evaluative. In automatic mode, the camera sets the standard matrix metering used more often than others. This is the most intelligent measurement

Question 47 Factual and legal basis. Evidence analysis.

From the book The Author's Lawyer Exam

Question 47 Actual and legal basis. Evidence analysis. Honest, reasonable and conscientious provision of legal assistance in any form, whether it be consulting, drafting various documents, representing interests or defending

9. Science at the service of toxicology. Spectral analysis. Crystals and melting points. Structural analysis by X-ray. Chromatography

From the book One Hundred Years of Forensics author Thorvald Jürgen

9. Science at the service of toxicology. Spectral analysis. Crystals and melting points. Structural analysis x-ray. Chromatography In the meantime, the events that took place in the trial against Buchanan became known throughout the world. With all disrespect for American science of those years, these

12.9. Matrix solution development method

From the book Systematic Problem Solving author Lapygin Yuri Nikolaevich

12.9. Matrix method of developing decisions Decision-making based on the matrix method is reduced to making a choice, taking into account the interests of all interested parties. Schematically, the decision process in this case looks like it is shown in Fig. 12.7. As we see, there is

4. Market research and analysis (analysis of the business environment of the organization)

From the book Business Planning: Lecture Notes the author Beketova Olga

4. Research and analysis of the market (analysis of the business environment of the organization) Research and analysis of the sales market is one of the most important stages in the preparation of business plans, which should answer questions about who, why and in what quantities buys or will buy products

5.1. Analysis of the external and internal environment of the organization, SWOT analysis

author Lapygin Yuri Nikolaevich

5.1. Analysis of the external and internal environment of the organization, SWOT analysis

8.11. Matrix method RUR

From the book Management Decisions author Lapygin Yuri Nikolaevich

8.11. Matrix method RSD Decision-making based on the matrix method is reduced to making a choice, taking into account the interests of all stakeholders. Schematically, the RUR process in this case looks like it is shown in Fig. 8.13. Rice. 8.13. The RUR model by the matrix method

4. Analysis of the strengths and weaknesses of the project, its prospects and threats (SWOT analysis)

author Filonenko Igor

4. Analysis of the strengths and weaknesses of the project, its prospects and threats (SWOT-analysis) When assessing the feasibility of launching a new project, a combination of factors plays a role, and not always the financial result is of paramount importance. For example, for an exhibition company

5. Political, economic, social and technological analysis (PEST-analysis)

From the book Exhibition Management: Management Strategies and Marketing Communications author Filonenko Igor

5. Political, Economic, Social and Technological Analysis (PEST Analysis)

11.3. Matrix strategy development method

From the book Strategic Management: tutorial author Lapygin Yuri Nikolaevich

11.3. The matrix method for developing strategies Development of an organization's vision The various states of the external and internal environment of organizations explain the diversity of the organizations themselves and their actual state. The multifactorial nature of the parameters that determine the position of each