How to solve inverse matrix of fourth order matrix

This is a lot of trouble
(A,E)=
-1 3 -7 10 1 0 0 0
-7 -3 5 10 0 1 0 0
3 1 -1 2 0 0 1 0
1 1 -1 2 0 0 0 1
r1-3r4,r2 3r4,r3-r4
-4 0 -4 4 1 0 0 -3
-4 0 2 16 0 1 0 3
2 0 0 0 0 0 1 -1
1 1 -1 2 0 0 0 1
r1 2r3,r2 2r3,r3*(1/2),r4-r3
0 0 -4 4 1 0 2 -5
0 0 2 16 0 1 2 1
1 0 0 0 0 0 1/2 -1/2
0 1 -1 2 0 0 -1/2 3/2
r1 2r2,r2*(1/2),r4 r2
0 0 0 36 1 2 6 -3
0 0 1 8 0 1/2 1 1/2
1 0 0 0 0 0 1/2 -1/2
0 1 0 10 0 1/2 1/2 2
r1*(1/36),r2-8r1,r4-10r1
0 0 0 1 1/36 1/18 1/6 -1/12
0 0 1 0 -2/9 1/18 -1/3 7/6
1 0 0 0 0 0 1/2 -1/2
0 1 0 0 -5/18 -1/18 -7/6 17/6
Exchange bank
1 0 0 0 0 0 1/2 -1/2
0 1 0 0 -5/18 -1/18 -7/6 17/6
0 0 1 0 -2/9 1/18 -1/3 7/6
0 0 0 1 1/36 1/18 1/6 -1/12
So a ^ - 1=
0 0 1/2 -1/2
-5/18 -1/18 -7/6 17/6
-2/9 1/18 -1/3 7/6
1/36 1/18 1/6 -1/12

Find the inverse matrix of order 3 and determinant of order 4
Finding inverse matrix 1 - 1
2 1 0
1 -1 0
Find determinant 1 0 2 0
-1 4 3 6
0 2 -5 3
3 1 1 0

0 1/3 1/3
0 1/3 -2/3
-1 2/3 -1/3
forty-five

Inverse matrix formula of elementary determinant
Eij (k) inverse = eij (- K)
Among them, eij (k) refers to the i-th line of the identity matrix multiplied by K and added to the j-th line, or the j-th line multiplied by K and added to the i-th line? See there are two different answers.. I only have so many wealth values

Eij (k) generally means that line j is multiplied by K and added to line I
This notation is not uniform. You just need to master it according to the definition method in the textbook
One's deceased father grind when do not need these notation, can give elementary matrix directly

Who can prove whether the inverse of elementary matrix is equal to the original elementary matrix
Is the inverse matrix of elementary matrix necessarily equal to the original elementary matrix, (E12) - 1 power equal to E12? Is it valid for all elementary matrices?

Not necessarily, the so-called elementary matrix refers to the matrix obtained by an elementary transformation of the identity matrix E. there are three types: (1) P (I, J), which means that the identity matrix e exchanges the elements of rows I and j, or exchanges the elements of rows I and J. its inverse matrix is itself, that is, P (I, J); (2) P (I (c)), which means that the

What's the Heisenberg matrix

Hessian matrix

The solution of inverse matrix
Let a satisfy a ^ 3-2a + e = 0, then (a ^ 2-2e) - 1=_________ .

Using the definition of inverse matrix: if the product of two matrices is unit matrix, then the two matrices are inverse to each other
That is, a (a ^ - 1) = e (where I use a ^ - 1 to represent the inverse of a)
We can rewrite the known conditions
A^3-2A=-E
(A^2-2E)A=-E
(A^2-2E)=（-E）/A
So the inverse matrix of a ^ 2-2e is - (a ^ - 1)

Who knows some proverbs about reading?

Read more than ten thousand books, write more than ten thousand words
There is a road to the mountain of books, and diligence is the path
Read a book a hundred times, and you will see what it means
There is beauty in the book, and there is a house of gold in the book
The more you read without thinking, the more you know; but the more you read without thinking, the less you know
Books are my slaves and must obey my will
Books can keep our childlike innocence; books can keep our youth
It's a man's time to study. Black hair doesn't know how to study early, but white head regrets how late he studies
If you are a sex addict, you will have a firm ambition: the old book addict must be good at writing, and the art addict must be good at skills -- Pu Songling's a Bao
The book is as rich as the sea, and there are all kinds of department stores. People can't take all their energy, but they can get what the spring wants. Therefore, I hope that scholars will make one-sided request every time
When reading a paragraph, you need to read it brilliantly. You need to keep your spirits up, erect your muscles and bones, and don't be sleepy. If you have a sword behind you, you need to see through the middle of the paragraph. When you hit the beginning, you need to answer the end, and when you hit the end, you need to answer the beginning. You can't just press the book. If you cover the book, you will forget it
There are three arrivals in reading, which are heart, eye and mouth. If the heart is not here, the eyes are not careful. The heart is not specific, but it is only reading. It can never be remembered for a long time. Among the three arrivals, the heart is the most urgent. When the heart arrives, the eye and mouth will not arrive
Learning is more important than learning It is better to know ten things but not to the ground than to know one thing but to the ground. -- Dai Zhen's chronicle of Mr. Dai Dongyuan
Reading is the best way to read. It's the worst way to learn
The omnipotent man is really nothing, and the expert who is expert in everything is really nothing ——Collected works of Tao Fen by Zou Tao Fen
Step up your study, grasp the center, be more refined than miscellaneous, be more specialized than more. - "selected works of Zhou Enlai" by Zhou Enlai
Reading is like mining, "gold in the sand" - Zhao Shuli
When I read a book about a subject I don't understand, I use the method of first obtaining the superficial view of the subject, first browsing many pages and chapters, and then rereading it from the beginning in order to obtain precise knowledge. At the end of reading the book, I understand its cause. This is the only positive solution I can introduce to you
To find out what can lead you to the deep in the books you read and to throw away everything else is to throw away everything that overburdens your mind and will lure you away from the main points
"Books are the annals of human beings. They pass down the countless and rich experiences accumulated by the whole mankind from generation to generation." - kanyeli
"Books are lighthouses standing in the vast ocean of time." - Whipple
"Books are good teachers to cultivate us. They don't need to be whipped or beaten, spoken or reprimanded, and they don't charge tuition fees or stick to forms." - d'Urbervilles
"Books are the ladder of human progress." -- Gorky
"The ideal book is the key to wisdom." -- Tolstoy
"Excellent books are the precious milk of nurturing outstanding talents. They are preserved as human wealth and serve for the further development of human life." - Milton
"Books are the accelerator of life." -- Nikolayeva
"Book is the spiritual legacy of this generation to the next generation." - Herzen
Book is the ladder of human progress -- Gorky
Books are the president of human knowledge -- Shakespeare
Books are the treasure house of human thought
Books the treasure of the world Thoreau
Good books are the most valuable treasure
Book is the only thing that never dies
Books make people master of the universe
In the book lies the soul of the whole past Carlisle
The influence of man is short and weak, but the influence of book is wide and far-reaching -- Pushkin
People can't live without books, just as they can't live without air
Book is not only life, but also the source of present, past and future cultural life -- kufayev
Books lead us to the most beautiful society, and make us know the great wise man of all ages - simmers
Books are such tools to transform the soul. What human beings need is enlightening nourishment. Reading is just this nourishment Hugo
Books are lighthouses standing in the sea of time
Books: the real university of today Carlisle
Books inspired my wisdom and soul. They helped me get out of the rotten mire. Without them, I would drown in it and be choked by stupid and vulgar things - Gorky
Books are like a magic lamp, which lights up the furthest and darkest way of people's life - wupitt
Books have the ability of immortality. They are the most lasting fruits of human activities
An ideal book is the key to wisdom -- Leo Tolstoy
Except for the barbaric countries, the whole world is ruled by books -- falter
Books are the ever burning lamps for the accumulation of wisdom
Books can lead us into a noble society and meet the greatest person of all ages - smiles
Books make people think freely
Only books are immortal
Books make us the inheritors of the spiritual life of the past ages
Books are the legacy of genius, handed down from generation to generation, but also a gift to those who have not yet been born - Edison

How to solve inverse matrix of fourth order matrix