Using elementary transformation, the inverse matrix of matrix A = {(1,2,3), (2,2,1), (3,4,3)} is obtained A is a third order matrix

Using elementary transformation, the inverse matrix of matrix A = {(1,2,3), (2,2,1), (3,4,3)} is obtained A is a third order matrix

1、 The matrix A is regarded as a column vector, and is written as a matrix composed of column vectors: 2,1,4,3, - 1,1, - 6,6, - 1, - 2,2, - 9,1,1, - 2,7,2,4,4,9. Second, exchange the first and fourth rows, and do not change the rank of the matrix: 1,1, - 2,7, - 1,1, - 6,6, - 1, - 2,2, - 9,2,1,4,3,2,4,9. Third, use elementary row transformation, Operate the matrix: add the first row to the second row; add the first row to the third row; multiply the first row by - 2 and add it to the fourth row; multiply the first row by - 2 and add it to the fifth row, so that the last elements of the first column are 0:1,1, - 2,7,0,2, - 8,13,0, - 1,0, - 6,0, - 1,8, - 11,0,2,8, - 5; 4. Continue the row transformation, multiply the second row by 0.5 and add it to the third row, Also add to the fourth line; multiply the second line by - 1, then add to the fifth line: 1,1, - 2,7,0,2, - 8,13,0,0, - 4,0.5,0,0,4, - 4.5,0,0,16, - 18, five, add the third line to the fourth line, add the third line four times to the fifth line: 1,1, - 2,7,0,2, - 8,13,0,0, - 4,0.5,0,0, - 4,0,0,0, - 16, six, add the fourth line four times to the fifth line: 1,1, - 2,7,2, - 8,13,0,0,0,0, - 4,0,5,0, The first line is 1,0,2,0.5,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 6,0,0,1, - 0.125,0,0,0,1,0,0,0,0,0, 10、 The first line: 1,0,0,0,0,0,0,0,0,75,0,1,0,1,0,6,0,0,0,0,0,1,0,0,0,0,0,0,0,0.11, the matrix is transformed into a ladder matrix by elementary transformation, and the number of non-zero lines is the rank of the matrix, so the rank is 4; because  o  o  o  o  o ; it shows that there is a case in the food of the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food, the food the results show that: 1; In this paper, we will introduce the methods of the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, the first, this is the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57534; the first case of the people's Republic of 57722; the first case of 57628; and the first case of 57628; 57628; 57628; ;;;;;;;;;;;;; 57628; \; 57628;; \57; &; &; &#And it will be 57628;; 57628;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; 943; adhere to the principle of "Tu Kuo Chou" and "Na Si Qia"

Using elementary transformation method to find the inverse matrix A-1 of matrix A = row 1 (- 100) row 2 (11-1) row 3 (13-2)

(A,E)=
-1 0 0 1 0 0
1 1 -1 0 1 0
1 3 -2 0 0 1
r2+r1,r3+r1
-1 0 0 1 0 0
0 1 -1 1 1 0
0 3 -2 1 0 1
r1*(-1),r3-3r2
1 0 0 -1 0 0
0 1 -1 1 1 0
0 0 1 -2 -3 1
r2+r3
1 0 0 -1 0 0
0 1 0 -1 -2 1
0 0 1 -2 -3 1
So a ^ - 1=
-1 0 0
-1 -2 1
-2 -3 1

Using elementary transformation of matrix to find inverse matrix of square matrix: [3 21] [3 15] [3 23]

(A,E) =|>|3 2 1 1 0 0||3 1 5 0 1 0||3 2 3 0 0 1|=|>|1 2/3 1/3 1/3 0 0||1 1/3 5/3 0 1/3 0||1 2/3 1 0 0 1/3|=|>|1 2/3 1/3 1/3 0 0||0 -1/3 4/3 -1/3 1/3 0||0 0 2/3 -1/3 0 1/3|=|>|1 2/3 1/3 1/3 0 0||0 1 -4...