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Linear Programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear Programming through its application has become one of the important and complex areas in Statistics. Linear programming is a widely used field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Linear programming was used extensively to deal with transportation, scheduling, and allocation of resources subject to certain restrictions such as costs and availability.
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Here in this course, my favorite topic was "Matrix addition and scalar Multiplication "because I fell very much comfortable on compared to all other topic's and in this topic, I learned a lot of new and exciting thing like Matrix, Dimension, Entries, Row Matrix, Column Matrix, and Square Matrix and many more and They are adding two matrices by adding the corresponding entries together is known as matrix addition in mathematics. In linear algebra, scalar multiplication is one of the fundamental operations that define a vector space. The Scalar multiplication of a real Euclidean vector by a positive actual number multiplies the magnitude of the vector without changing its direction in everyday geometrical contexts.
And coming to the learning part, I learned a lot of topics such as Matrix sum, Matrix addition, and more and more topic's a
I have learned many outcomes, such as Defining the vector space Mmn of m*n matrix, Discovering several properties of transpose, and Discovering the alternative ways to compute matrix products. Many outcomes are there, And solving many examples that are listening to it helped me a lot for learning practically and getting confidence in my subject.
And, especially coming to Graph Adjacency Matrix, it was a great topic in this "Matrix addition and scalar Multiplication "because the adjacency matrix of a simple labeled graph, also known as the link matrix, is a matrix with rows and columns marked by graph vertices and a 1 or 0 in place depending on whether and are adjacent or not. The adjacency matrix for a simple graph with no self-loops must have 0s on the diagonal. The way it designed was to give me some more interest in this topic which boosts my confidence for solving n number of problems in exam's
Here in this course, "Determinants of Matrix" is a challenging topic for me. I feel hard because The majority of determinant problems are restricted to 3x3 matrices. Larger matrices are seldom used because the complexity of the equation increases approximately proportional to the factorial of the number of dimensions. To convert the matrices into triangular matrices. Since the Determinant is the same if determined from rows or columns, the triangular matrix has a column with just one non-zero entry, which is on the main diagonal, regardless of its dimensions. Even though it was thought to be difficult, I have mastered a few topics.
Such as Determinants of matrix size 2, Determinants expansion along rows, Determinant of transpose, Determinants expansion along with columns, Determinant with zero rows or column, and Determinant with zero rows or column swap and I very comfortable with all these topic's and a few are left which I haven't mentioned and now coming to parts that still need work
Such as the Elementary matrix and all the sub-topics in the elementary matrix, and the next topic was properties of Determinants of the matrix, Determinant respects matrix multiplication, and How EigenValues are Change with a Matrix, the following was Properties of similar Matrices, and finally Matrix Diagonalization, So, here are the topic's that I was still ned to work on and for mastering this topic's I need some more and clear examples which will help me for getting the confidence of these topics.
And I will also put extra time to get confidence and master all the above-listed topics, and it will be great sir; if you can, please explain it once again with some more practical examples so that it will be helping me a lot on master this vast topic.
Here in this course, “Vector Operations” is the most helpful topic in the whole system, which helped me learn all the remaining topics because, Operations on vectors, The rules of elementary algebra are extended to vectors. Addition, subtraction, and three forms of multiplication are among them. The diagonal of the parallelogram built with the two initial vectors as sides are the sum of two vectors, which is defined as a third vector. When a vector is multiplied by a positive scalar (i.e., a number), the scalar multiplies the magnitude of the vector while leaving the direction unchanged (if the scalar is negative, the order is reversed)
And it was beneficial in all other courses which are done in previous, now and also in future too because:
Vector analysis is a mathematics branch that covers both the quantity and the direction. Scalars are physical and geometric quantities defined entirely in the required measuring units by specifying their value. Thus, measurement of mass in grams, measurement of temperature in degrees by scale, and time measurements in seconds are possible. Leaves can be defined graphically on numeric points such as a clock or thermometer. Often known as vectors, some amounts require a definition of both direction and size.
Vectors include things like velocity, force, and displacement. A guided line segment, symbolized by an arrow pointing in the direction of the vector quantity, can be used to graphically represent a vector quantity, with the length of the segment representing the magnitude of the vector.
And, here finally, in hole courses that I have done and hole topics I have done till now, I felt that vector operations are beneficial in all the studies.
Here is the few most important result which I get on doing “ Linear Algebra course “ In many fields of science, linear algebra is significant in general. Since linear equations are so simple to solve, virtually all areas of modern science include models that approximate equations by linear equations (using the arguments for Taylor extension) and that solving a system helps to establish a theory. You and I have no idea how people use the power of linear algebra to approximate solutions to equations. They would not be vital if they were to make a list. Since the solution of equations is in most cases synonymous with the resolution of a problem in practice, this could be extremely useful. For that reason, algebra has a reason, and it is reason enough to know linear algebra by every scientist.
Of course, Linear algebra is used in mathematics in abstract algebra, and vector spaces appear in many fields, including the theory of the group, ring theory, module theory, representation theory, theory of Galois, and much more. Understanding the tools of linear algebra enables one to better grasp these theories, and some theorems of linear algebra often need to understand specific approaches.
And, the reason why I believe these results are essential because, In addition to algebra, the infinite-dimensional version of linear algebra is also a large part of functional analysis. Many of the finite-dimensional theorems break down excitingly; we retain some of our intuition, but much of it breaks down. Of course, no algebraic understanding is lost, but most analytical components do; closed balls are never compact. Rules are not always the same, and the space structure varies a lot depending on the standard you use. Therefore, knowledge of linear algebra is essential even for anyone learning analysis.
Here in this course, it was designed in very well structured and perfect way of the topic’ and examples so that students will not face any issues while learning the course. In my opinion, I felt a very fantastic feeling while knowing the path and content in it. Every problem and its application and theory behind it was clearly stated in a very well-structured manner.
For suppose if you can see one of the topics listed in our course, such as “ Classification of Finite-Dimensional Vector Spaces,” here the topic was clearly explained and also stated with theorem behind it and explanation of every variable :
And further, it was also explained with practical examples So that we can get both theoretical and practical knowledge.
Here the complete course curriculum and its structure of stating every example and its application and arranges if all the concepts can be more interactive for students to learn more effectively and fun.
And, here the complete course was designed with the help of different learning strategies such as:
1) Sequence Learning: teach students how to order the data by alphabet or numerical means:
Teach timelines, follow orders, outlines, and maintain structured content.
2) Dual learning: teaching students how similarities can classify materials.
Web content defines, discusses, and uses flow charts and diagrams.
3) Verbal Learning: Learn how to handle ideas aloud to students.
Provide students opportunities for individual or group discussions to proceed with ideas verbally.
So, finally, by applying different possible strategies, this course was designed in a well-structured and constructive manner so that every student can benefit from it
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What Is Linear Programming?
Linear programming, also called linear optimization, it is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.
Is assignment problem is a linear programming problem?
An assignment problem is a particular case of transportation problem. The main motive is to assign a number of resources to an equal number of activities, so that we minimize total cost or maximize total profit of allocation.
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