Transpose matrix 3x3. Matrix transpose in Microsoft Excel

The transposition of the matrix through the Danish online calculator will not take a lot of an hour, but then you can quickly give the result, and you can also use it more beautifully in the process itself.

In some cases, in the calculation of algebra, there is a need to remember in small numbers the rows and hundreds of matrices. Such an operation is called matrix transpose. Rows in order are stacked in hundred percent, and the matrix itself is transposed. They have a number of rules, and they have a problem and learn more about the process, speed up the online calculator. In the sutta, you will be able to learn more and more beautifully to master the theory of transposing matrices. A significant advantage of this calculator is the demonstration of the open and detailed solution. In such a rank, I’d reject more and more knowledge about the development of algebra. Until then, you can be reconsidered for what you help me, if you have successfully fit from the factory, I will hand over the transposition of the matrix.

Vikoristovuvati calculator is simpler. To know the transposed matrix online, set the size of the matrix to the onslaught on the "+" or "-" icons until the required value of the number of hundredths and rows is removed. Enter the required numbers near the field. Below, the button "Enumerate" has been swapped out - її the onslaught to bring to the screen is ready to solve with the detailed encryption algorithm.

Matrix А -1 is called a ring matrix in relation to matrix А, if А * А -1 = Е de Е is a single matrix of n-th order. Zvorotna matrix can be used for square matrices.

Appreciated to service... For help given to the service in the online mode, you can know the complement of algebra, the transposed matrix A T, the conjugate matrix and the rotary matrix. The decision is carried out without the need to be on the website (online) and without a website. The results of the calculation are drawn up at the Word format and in Excel format (that is, the ability to reconfigure the solution). div. the butt is formalized.

Instructions. To reject the solution, it is necessary to set the size of the matrix. In the new dialogue window, you have to store the matrix A.

also Zvorotnya matrix by the Jordano-Gauss method

Algorithm for knowing the ring matrix

1. The important transposed matrix AT.
2. Viznennya dodatkіv algebra. Replace the skin element of the matrix with a complementary algebra.
3. Skladannya ring matrix from the algebra data: the skin element of the rimmed matrix to be sent to the viewer of the output matrix. Resultuyuyu matrix є revolving for the output matrix.

Offensive algorithm for knowing the ring matrix analogous to the one in front of the front for a vignette of deyaky crocs: a list of counts algebraic supplements and then the allied matrix C starts.

1. First, chi is a square matrix. If not, then the ringing matrix is ​​not sleepy.
2. Calculation of the matrix designator A. Yaksho vin is not expensive to zero, the solution is good, but not the verbal matrix.
3. Viznennya dodatkіv algebra.
4. Storing allied (mutually, attributed) matrices C.
5. Folding of the verbal matrix from the algebra supplements: the skin element of the attached matrix C is sent to the visual matrix of the input matrix. Resultuyuyu matrix є revolving for the output matrix.
6. To cheat the misconception: multiply the output and the negated matrix. As a result, one matrix is ​​to blame.

Butt number 1. Writable by the matrix at the viewer:

Algebraic supplements. ∆ 1,2 = - (2 4 - (- 2 (-2))) = -4 ∆ 2,1 = - (2 4-5 3) = 7 ∆ 2,3 = - (- 1 5 - (- 2 2)) = 1 ∆ 3.2 = - (- 1 (-2) -2 3) = 4

A -1 =

0,6 -0,4 0,8 0,7 0,2 0,1 -0,1 0,4 -0,3

The first algorithm for knowing the ring matrix

I am guided by the scheme of the ring matrix.

1. We know the size of the square matrix A.
2. We know the complement of algebra to all elements of the matrix A.
3. I will write down the additions of the algebra of elements of rows in the hundredths (transponding).
4. Dilimo skin element of the trimmed matrix on the matrix format A.

Yak bachimo, the transposition operation can be stuck on the cob above the outgoing matrix, so in the beginning over the discarded algebraic supplements.

Special vipadok: Zvorotn_y, according to the relation to the single matrix E є the single matrix E is.

To transpose the matrix, you need to write the rows of the matrix in 100%.

Yaksho, then the matrix is ​​transposed

Yaksho then

Zavdannya 1. Know

1. Square matrix holders.

For square matrices, a number is entered, as it is called a visnatnik.

For matrices of a different order (size), the matrix is ​​set by the formula:

For example, for the matrix

butt . Count the matrix labels.

For square matrices of the third order (size), there is a trikutnik rule: a dotted line means multiplying a number, through which a dotted line passes. The first three numbers are required, the next three numbers are required.

butt... Calculate the visnatnik.

Schob give the hallmark of the viznachennya, you need to send the clearer to the minor and the algebraic supplement.

Minor The element of the matrix is ​​called a visnatnik;

butt. We know the actions of the Minor Matrix A.

Algebraic additions The element is called a number.

Otzhe, as the sum of indexes and pairs, then nothing can be seen. If the sum of indexes is unpaired, then it seems like a sign.

For the front stock.

Matrix template to be called the sum of the creation of the elements of the deyakogo row

(Stovptsya) on їх algebraic add-ons. The price is visible on the matrix of the third order.

The first entry is called the layout of the visitor in the first row, the other is the distribution in another hundred, the last one is the layout in the third row. The number of such distributions can be recorded in a number of developments.

butt... Calculate the visnatnik according to the rule of tricycle and open it in the first row, then in the third hundred, then in the other row.

Place the card holder in the first row:

Distribution card for the third hundred:

Place the viznachnik in a different row:

Remarkable, for more than zero, it is simpler to calculate. For the first time, spread out according to the first hundred, otrimaєmo

Among the powers that be made are the power, which allows the possession of zero, but itself:

Even before the elements of the row (one hundred percent) are added to the element of the first row (one hundred percent), multiplied by a nonzero number, then the design card does not change.

However, it is possible to use a form-holder and accept zero, for example, in the first row.

Vishnachniki of other orders are counted in the same way.

Zavdannya 2. Number the card holder in the fourth order:

1) rozklavshi be-like a row, or be-like a hundred

2) having rinsed off the front zeros

Otrimaєmo dodatkovy zero, for example, at another hundred. For a whole element of another row, multiply by -1 and dodamo up to the fourth row:

1. Determination of systems of linear algebraic equations by Cramer's method.

It is shown how the system of linear algebraic equations is connected by Cramer's method.

Zavdannya 2. Rozv'yazati the system of rivnyans.

Require to count the chotiri viznachniki. The first to be called the main one and to stock up on performances when they are not homeless:

It is great that the system cannot be violated by the Cramer method.

Three of the largest business cards are known, and go by replacing one hundred percent to one hundred right-hand parts.

We know. For the first time, the first place is important for the minimum number of the right parts:

We know. For many other people, it is important to note the name of the one hundred percent of the right parts:

We know. For the third hundredth, it is important to designate the miniamo for one hundred percent of the right parts:

The solution of the system is known from the Cramer formulas:,,

Such a rank of solution of the system,

An overwhelming change, for the whole knowledge of the solution is presented on all the system.

1. Verification of systems of linear algebraic equations by the matrix method.

As a square matrix, the matrix is ​​not expensive to zero, but it is a rotary matrix, so it is. The matrix is ​​called single і maє viglyad

The zvorotna matrix is ​​behind the formula:

butt... Know the rotary matrix to the matrix

The collection is numbered in the form of a designer.

We know the additions of algebra:

I can write down a rotary matrix:

Shcheb pereviriti calculation, need perekonatisya, shho.

Let the system be given lіnіynykh rіvnyany:

Significantly

Todi system can be written in matrix form yak, and zvidsy. The formula is called the matrix method of interconnecting the system.

Zavdannya 3. Virishity system in a matrix way.

It is necessary to read the matrix of the system, to know it to be effective, and then to multiply it by a hundred right parts.

The zvorotna matrix is ​​already known in the front butt, so it is possible to know the solution:

1. Verification of systems of linear algebraic equations by the Gaus method.

Cramer's method and the matrix method are used only for square systems (the number of equal ones for the number of non-native ones), and the designer is not responsible for the amount of zero. Even the number of people who are not home to the number of people who are not home to them, or the originator of the system is zero, the Gauss method is used. Gaus's method can be used for verifying any systems.

І is presented on the persha ryvnyannya:

Zavdannya 5. Razv'yazati the system of rivnyans by the method of Gauss.

According to the neglected matrix, the system is updated:

We know the decision:

When robots with matrices are used, it is necessary to transpose, tobto, speak in simple words, turn over. Surely, it is possible to kill the tribute by hand, Aleksel will proponate the way in which to grow, it is simpler and more sophisticated. Let's take a look at the report.

The transposition of the matrix is ​​the whole process of changing the rows and rows. Have Excel programs There are two possibilities for carrying out the transponder: the vicious function TRANSPOSE that for an additional tool of a special insert. It is easy to see the skin from the cich options in the report.

Method 1: operator TRANSPOSE

Functions TRANSPOSE be classified as operators "Posilannya ta masivi"... Especially those who are in it, as in their functions, which work with the arrays, the result of the visualization is not in the place of commerce, but in the array of danikh. The syntax of the function to make it simpler is as follows:

TRANSPOSE (array)

So, let's use the argument of the second operator per array, in our case, the matrix, which is the next one to re-create.

Surprisingly, you can use a real matrix to fit the function.

1. Seeing non-filling in the middle of the archway, planning to build up the extreme upper ones in the middle of the reworked matrix. Dali embossed on the icon "Insert function", scho the sewing near the row of formulas.



2. Running Mainstream functions... Vidkrivaєmo in a new category "Posilannya ta masivi" abo "New alphabetical list"... For that, I will name yak "TRANSP", Vyroblyaєmy my vіdіlennya i embossed on the button "OK".



3. The launch of the window of arguments in the function is displayed TRANSPOSE... For one argument of the given operator, the field "Massiv"... Before it is necessary to enter the coordinates of the matrix, as it should be turned over. For the whole, I will set the cursor at the field, pressing the mouse button to the left, you will see the entire range of the matrix on the arch. For that, the address of the region appeared in the arguments, click on the buttons "OK".



4. Ale, yak bachimo, at the commander, the yak is designated for the result, it seems that the meaning is incorrect in the view of the mercy "VALUE!"... There are some special features of robotic operators of arrays. To correct it, you see the range of mid-range, for which the number of rows has a large number of cob matrices, and the number of hundred is a number of rows. The type of appearance is even more important to ensure that the result appears correctly. At the same time, in the middle, in which to take revenge viraz "VALUE!" It is the fault of the top one that was seen in the middle of the array, and the next step was to fix the procedure of seeing by pressing the button of the Misha. In addition, when you saw the video, move the cursor to the row of formulas immediately to send the operator violated TRANSPOSE, scho can be seen at niy. Writing, schob counting, you need to press not a button Enter, as it is established at the usual formulas, but dial a combination Ctrl + Shift + Enter.



5. Pislya qih diy the matrix was represented as we need it, to the transposed view. Alas, there is one more problem. On the right, there is now a new matrix є of dressings with the formula of arrays, which cannot be changed. When trying to change the matrix instead of the matrix, there will be a viskakuvati pomilka. The deyakykh koristuvachіv such a camp of speeches is completely satisfied, so that the stink doesn’t get in the way of snakes in the array, and the axis is in need of a matrix, which can be done effectively.

   For that schob virishity qi problem, Vidіlyaєmo all transpositions range. By moving to the tab "Golovna" klatsaєmo by pictogram "Copy", yaka roztashovana on page at the group "Buffer exchange"... It is possible to replace the said action by seeing the output of the standard set of keys for copying Ctrl + C.



6. Therefore, not knowing the view from the transposed range, click on the new right mouse button. At the context menu of the group "Paste Parameters" klatsaєmo by the end "Significance", yaka maє viglyad pictograms from the pictures of numbers.

   

   Writing the formula to the array TRANSPOSE It will be seen, and in the midst of the middle you will be deprived of one meaning, with which it is possible to do so by itself, as with the outward matrix.

Method 2: transpose matrix for additional special insertion

In addition, the matrix can be transposed with the help of one element of the context menu, which I will call "Special insert".

The matrix has been reimagined if the meanings on the arc are lost.

In two ways, about what kind of thing, you can transpose in Excel both matrices and tables. The procedure will be practically identical.

Then, we found out that in the Excel program the matrix can be transposed, so to turn it over, remembering the hundred and fifty rows in two different ways. The first option of transferring the victorian function TRANSPOSE, and the other is special insertion tools. Behind a great rakhunk, a dazzling result, which can be done with both victorious ways, does not happen at all. Offense methods of cleaning are practical in any situation. So, when choosing a variant of the revision to the first plan, go to the specials of the transfer of a particular koristuvach. Tobto, whichever of these methods are especially good for you, you must be victorious.