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                                                           Applications of matrices in computer science pdf
    An array is defined as a rectangular number or symbol matrix that is usually arranged in rows and columns. The array order can be set to the number of rows and columns. Entries are numbers in an array known as an element. The plural of arrays is an array. The array size is marked as a n by m array and is entered × in which n= number of rows and m=
    number of columns. Example:\[\begin{bmatrix} 6 & 4 & 24\\ 1 & -9 & 8 \end {bmatrix}\]The matrix above has 2 rows and three columns. Array types What are different types of arrays? There are different arrays. Here they are -1) Row Matrix2) Column Matrix3) Null Array4) Square Matrix5) Diagonal Matrix6) Upper Triangle Array7) Lower
    Triangular Array8) Symmetrical Array9) Symmetrical ArraySent Actions Matrices:Assume, that we have two arrays: A and B.Both arrays A and B have the same number of rows and columns (i.e. the number of rows is 2 and the number of columns 3) so that they can be added. With simpler words, you can easily add a 2 x 3 array with a 2 x 3 array or a 2 x 2
    array with 2 x 2 arrays. Keep in place, however, that you cannot add a 3 x 2 array with a 2 x 3 array or a 2 x 2 array with a 3 x 3 array. A = \[\begin{bmatrix} 1 & 2 & 3\\ 7 & 8 & 9 \end {bmatrix}\] B = \[\begin{bmatrix} 5 & 6 & 7\\ 3 & 4 & 5 \end {bmatrix}\]A + B = \[\begin{bmatrix} 1 + 5 & 2 +6 & 3 + 7\\ 7 + 3
    & 8 + 4 & 9 + 5 \end {bmatrix}\]A ÷ B = \[\begin{bmatrix} 6 & 8 & 10\\ 10 & 12 & 14 \end {bmatrix}\]Note : Keep in place that the order in which arrays are inserted is not important; therefore, we can say that A + B is equal to B + A.We are considering a simple multiplication of 2 × 2 arrays A= \[\begin{bmatrix} 3 & 7 \\ 4 &
    9 \end {bmatrix}\] and repeat array B= \[\begin{bmatrix} 6 & 2 \\ 5 & 8 \end {bmatrix}\]Now we can calculate each part of product matrix AB as follows:AB11 product = 3 × 6 + 7 ×5 = 53 AB12 product = 3 × 2 + 7 × 8 = 62 AB21 product = 4 × 6 + 9 × 5 = 69 AB22 product = 4 × 2 + 9 × 8 = 80Fore matrix AB equals,AB = \[\begin{bmatrix} 53 & 62 \\
    69 & 80 \end {bmatrix}\]MatricesMatrices has many applications in various fields of science, commerce, and social science. Arrays are in use:(i) Computer graphics (ii) Optics (iii) Cryptography (iv) Economics(v) Chemistry vi) Geology (vii) Robotics and animation (viii) Wireless communication and signal processing (ix) Use of finance ice(x) Use of
    mathematics Matrixes In computer graphics Architecture, cartoons, automation was done by hand drawings, but today they are done on a computer. Square arrays very easily represent the linear conversion of objects. They are used for 3-D images in two-dimensional layers in the field of graphics. In the graphic, the digital image is initially treated as an
    array. Array rows and match rows and columns of pixels, as well as numeric annotations pixel color values. Using arrays to manipulate a point is a common mathematical approach to video game graphics Matrix is also used to indicate charts. Each chart can be represented as an array, each column and each row in the array is a node, and their intersection
    is the strength of the relationship between them. The graphic uses array functions, such as rotation, rotation, and compaction. To convert a point, we use the equation Use of arrays in cryptographyCryptography is a technique to encrypt data so that only the relevant person can obtain the data and paste the data. In previous days, video signals were not used
    for encryption. Anyone with a satellite plate was able to watch videos that could lead to the loss of satellite owners, so they began encrypting video signals so that only those with video ciprits can decipt signal encryption. This encryption is done using a reverse key that is not inverted, encrypted signals cannot be encrypted, and cannot get back to their
    original format. This process is done using a matrix. A digital audio or video signal is first taken as a sequence of numbers representing the variation in atmospheric pressure of an acoustic sound signal over time. Filtering techniques that depend on array multiplication are used. Use of arrays in wireless communication Used to model and optimize wireless
    signals. The detection, extraction and processing of data embedded in the signal matrix is used. Arrays play a key role in signal evaluation and detection problems. They are used to process signals in the sensor system and design an adaptive filter. Arrays help you work with and represent digital images. We know that wireless communications and
    communications are an important part of the telecommunications sector. The sensor system's signal processing focuses on signal enumerment and source positioning applications and is very important in many areas, such as radar signals and underwater surveillance. The main problem with sensor system signal processing is detecting and locating radiant
    sources based on time and location data collected from sensors. The use of matrices in ScienceMatrices is used in optics science for reflection and art. The matrixes are also useful in electrical circuits and quantum mechanics, as well as in electrical energy equivalent conversions. Arrays are used to solve the equations of the AC network of electrical circuits.
    The application of the matrix in mathematics The application of the matrix in mathematics has expanded the application in solving linear equations. Matrix is incredibly useful things that happen in many different spread areas. The application of matrices in mathematics applies to many disciplines, including different mathematical disciplines. Engineering
    mathematics is applied in our daily lives. Using matrices with triangle surface pool We can use the matrix for any finding an area the vertage of the triangle is given. Let's say we have a triangle ABC with vertage A(a,b) , B(c,d) , C(e,f)Now triangle RANGE ABC , Triangle Range ABC can be given by determining factor= \[\frac{1}{2} \begin {bmatrix} a & b
    & 1\\ c & d & 1 \\ e & f & 1\end {bmatrix}\]You can check where all three dots are collinear or not. The ellipses are assumed that A(a,b), B(c,d), C(e,f) are choinary if they do not form a triangle, i.e. the triangle range must be zero. Points A,B,C are collinear if \[\begin{bmatrix} a & b & 1\\ c & d & 1 \\ e & f &
    1\end {bmatrix}\] is lost. When most people think of the word matrix, they probably think of a 1999 film starring Keanu Reeves. The film relates to the mathematical concept of arrays only to the extent that the film's ominous computers use the use of matriles, as many real-life computers do. In fact, matriles are applications in computer science because they
    are a convenient and compact way to represent large number sequences. Some economic theories may also be well represented with matries. In mathematics, the principles of matricity are essential for chart theory and actual analysis. This guide begins by considering a small matrix, namely those with two columns and two rows. The topic begins with
    detailed instructions on how to describe them and how to ×2 arrays. It also explains how these concepts can be used for access to information. The second topic in this guide generalizes information about the first section to all arrays. It ends with the introduction of line reduction strategies to solve the matrix and a few other more advanced topics used in
    other areas of mathematics. Introduction 2×2 The MatricesA 2×2 matrix has two rows and two columns. They have some similarities to tables because they have rows and columns, but they have crucial differences. Tables are meant to be graphical displays. They can be manipulated to display information in certain lights, but the actions between the tables
    make no sense. On the other hand, arrays are a set of numbers. There are no hard breaks between numbers, as in the table, and there are ways to perform actions using a matrix. However, array functionality is more involved than basic mathematical functions that are used to add, gradually, tell, and share individual terms or even functions. This is partly
    because the matrix typically contains many elements (also known as events), and actions are usually performed with other arrays, except for scalar multiplication. However, it is possible to increase, reduce, multiply and take matrix powers with certain limitations. It is also possible to find some matrices reversed. This topic introduces these concepts 2×2
    before generalising them to an array of any size in the next section. It starts with a description of the matrix, and then Add, subtraction, scalar multiplication, and array multiplication. It then deals with × 22 identity matrix above and its features. The following section discusses the active substances and how they can be used to find whether the matrix is
    reversed and, if so, what it is. Finally, the topic ends with ways in which the matrix can be mathematically used to represent information. Description of matricesEqual MatricesTypes of MatricesMatrix insertion and reduction types The concepts presented in the first topic of the MatricesEquationMatrix MultiplicationIdentity MatrixDeterminant of a MatrixSingular
    MatrixSolving a System of EquationsRepresenting Information Introduction to Other Matrices2× may be extended to other matrices. Technically, an array can have an infinite number of rows and columns, and an array with m-rows and n-columns is called an m x n array (read m by n). Presentations in a global matrix typically contain elements with two
    subscripts. The first represents the element row and the second represents the element column. For example, the first element in the upper-left corner of a global array would have a subscript of 11, while an element in the lower-right corner of the m x n array would have the subscript mn indicated by the image. Matries that represented knowledge in
    substances such as computer science can be huge, when in fact they are a condensed and convenient representation. Although there are a lot of steps involved in multiplicing arrays, there are repeating algorithms that programs can use to calculate multiplicing of large-scale arrays. This section begins by generalizing the introduction to array and array
    actions. It then discusses how to find the dominant substances of 2x2 and 3×3 before generalising the process of any square matrix. This information is used to explain how reverse simplification and search for such arrays is possible. The topic also discusses how to use inverse to resolve equation systems represented by arrays. Finally, the topic ends by
    explaining the methods of reducing rows and other applications in the arrays. Introduction to matricesMatrix addition and subtractionMatrix Scalar MultiplicationMatrix MultiplicationIdentity MatrixDeterminant of a 2×2 MatrixDeterminant of a 3×3 MatrixSimplifying the DeterminantInverse of a 2×2 MatrixInverse of a 3×3 MatrixSingular MatrixSolving a 2×2
    Equation System Using the Matrix Reverse Method 3×3 Equation System Resolution matrix Reverse Gauss-Jordan Method Solving a Three-Linear Equation System Shrinking Matrix To Solve An Equation System Using Matrix Row Conversions Finding The Area of The Norm Constables Finding the Parallelogram Determining Range To Find a Triangle and
    Polygonal Area
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