[BOŞ_SES] Hello. Now, we begin the second part of our course in linear algebra. First part as a separate course, we have made as a separate unit. I would like to briefly introduce the structure. The issues we saw in Part 1 basic concepts. In Part 2, we will now begin the issues we saw in the course, applications of matrices and matrix as the application of these concepts. Basic concepts consists of two main categories. Linear spaces and linear processors. Linear spaces, a long, elements of cluster We define linear space with two process described above. Linear important space size. Here, determine the size, it can turn this space The number of independent vectors of a vector set. The two linear spaces and linear processor determining the relationship between processors. We see here the main title algebraic processors. But processors that differential differential equations taking or taking them to the integral equation integral processors, linear processor which belongs to the family. We introduce a general subject as a preparation and we determine its place in the general education mathematics linear algebra. After making two more preparatory department, in a concrete way this needs in linear algebra comes from, we try to identify them. These vectors in the first plane and that We have seen that there are many things we can learn. Vectors in the plane may seem very simple, but overall processed Almost all of the concepts of linear space there is in the plane. But the plane is not possible to make progress, because I need to draw the vector. And this, of course, we can do things drastically limiting. But increasingly the ones out here linear space and basic proposition here in two dimensions also need to draw non-limited as to be multi-dimensional We have seen in the space of infinite dimensional spaces and even be examined in this context. Infinite dimensional spaces, function spaces. Finite-dimensional space vector spaces, but a finite number of components It does not accept to be a limit. Again, as a concrete application We examined in detail the equations of two unknowns. Again, since this issue is one we all learned in middle school. But when we examine it a little depth, We see that all of the fundamental issues raised include the mmatris. We saw them. Then, we define a linear space as more abstract. We saw linear independence and bases topics in linear space. Functions as an application of the infinite-dimensional linear space We saw the Fourier series in the space. This is the plane i i j or in space, j, k we define the unit vector the base vector is nothing more than generalizations to infinite dimensions. Following this, we started from the linear processor, algebraic processors. However, further progress could be made, but the basic concept is very good We saw can be transferred. From there we went to the matrix. Here, we examine the overall matrix. We saw matrix operations. Collection of matrices, issues such as multiplying with each other. In Part 2, our lesson now beginning, Before we start by giving a summary of Part 1. Part 1 as an infrastructure but do not see it as a necessary infrastructure. Finally, business can be done with four processing and this course can be seen without this prerequisite. Here we will try to work with the matrix and in particular square matrix. So line with that of the matrix is equal to the number of milk. But lacking that knowledge in the basic subjects whether they can measure themselves, even if they apply themselves to learn whether the missing parts of the As part we could have given a summary of the first part. After that, progressively, we will see the matrix. Here of course the summary of the first part, No need to go over again, would suffice to bring it to your attention. Starting from the basic question as we are moving in question is in the department of mathematics. We say it is a language of mathematics. Sub language of mathematics, what infrastructure? Subdivisions, what units? After introducing them briefly, what are our tools? Our vehicles are four operations and its well in order to take the limit with small or large infinity forever. So you can do all the math down with it. Name of linear algebra is irrelevant. In linear algebra course, came from the west also called the Turkish language. The word algebra comes from the Arabic. Arrangements within the meaning of the term. And indeed the ideas of matrices, thoughts, good tool to edit data. He comes into the linear algebra sense. Of course there are also completely different topics in algebra but also in terms of matrices The idea of organizing defines fine. Analysis, and other operations, through the branches of mathematics, is infinitesimal analysis. There are limits to this concept. One works in linear algebra without limit. Here is a brief summary of the issues that I say here, I recommend you test one yourself. [BOŞ_SES] here Starting with vectors in the plane, we are expanding the overall size of the space. That you test yourself calmly, I encourage you to see if you know how. Knowing the basic issues, It will broaden your horizons and topics that will help you understand more deeply. Remind them as required by the scope of this course, we're moving. I said Fourre Series in infinite dimensional spaces. The respective department always helpful. Fourier series of important technological revolution in which we live today a data entry input from the mathematical basis of what we call digital revolution a wave, a sound, an image can expressed in numbers, here it comes to calculating their Fourier coefficients. After that show, the more abstract areas We're going to linear and linear transformations processors. Considering multivariate functions, a y = f (x) in x an odd number, If this year the number one single variable functions, as we see here. Opposed to coming to a curve in the plane. Multivariate numerical functions, It is beginning to be analyzed from several terminals. One end, that one component of the x, hence defining a vector with numbers; it's called a vector function. It comes opposed to a curve in space. Other end, y is a number, x variables be numbers; this is the simplest structure two-component vector x and y on a one- is simply a text component at that time as Z = f (x, y) call, showing a surface in this space. A step beyond that, instead of dependent variables we show u y, because they usually have physical elements; an electric current, a force, a moment, momentum, heat flow, magnetic size, physical size as the field. Of course, the physical quantities geometry x, y, z coordinates with and in terms of time is defined as t. So less mathematically feature of the vector field x and y, and few in number, but both the vector functions including multiple, multivariate functions in this still Coursera I have given Multivariate Functions The topics covered in the course. See also the following tip to the other end where we deal: this argument a is an odd number, the number being a single dependent variable, now this year is equal to f (x) to see if there are three elements to work x looked into the most simple, y have looked into the most simple, there is of course fun. What is the most basic form so f we think of them in these functions Being the simplest form of linear functions, linear function means The presence of these forces means that only the first argument. Then any y within the function of x You can write in terms of the first forces. Here are two indicators in the index, there's need for indices. Of an x, x1, x2, indicators to give xn, we call XJ. There are of course also need to know here the year in their indices. So here are a aija It composed two indicators specified sequence numbers. In this series i and j able to handle a two-dimensional array of thinking. This is also happening matrix. Our main issue with this is happening in this last part of the course. In a relationship with multivariate functions but extremely simple functions. Therefore, derivative, integral to them as well as information no need to require limits, subject can be done with four works. Now we continue this summary, that conversion show them another space without a space of vector to move and space to examine the relationship between these two elements. Equations are emerging in this context. Then this may be indicated by the number of conversions and here we come to the issue we see in matrices. Again, here is some basic information about the matrix After we're going to matrix operations. Equal to that of the two matrix matrix operations there, what are the relations with this transformation, to know them and requires learning and ends with it. As infrastructure, and basic information as required course material. This issue we handle Linear Linear Algebra Part 1. This was given as a separate course. Knowing that if this course of events, of course, possible, but make known dynamic, to better understand the development of ideas It may be possible. Now we want to work with square matrix. Square matrices might ask why. He had the privilege of square matrix. Before we begin determinant of square matrix. In the previous two parts of this duality that two We see it as a matter of unknowns we face in two equations. There are some privileges square matrices. Now we want to advance our issues, starting with those privileges. To give an opportunity to the first part of the summary To take a peek, now here I give you a call.