The matrix A = 2 - 1 - 1 1 2 1 - 2 1 4 4 - 6 2 - 2 4 3 6 - 9 7 9 is reduced to the simplest form by elementary row transformation The big God helps A= 2 -1 -1 1 2 ) 1 1 -2 1 4 ) 4 -6 2 -2 4) 3 6 -9 7 9)

The matrix A = 2 - 1 - 1 1 2 1 - 2 1 4 4 - 6 2 - 2 4 3 6 - 9 7 9 is reduced to the simplest form by elementary row transformation The big God helps A= 2 -1 -1 1 2 ) 1 1 -2 1 4 ) 4 -6 2 -2 4) 3 6 -9 7 9)

You are a matrix of how many times how many numbers to write

Using elementary row transformation to find a maximal independent group of column vector group of matrix A = (2 - 1 - 11 2; 1 1 - 2 1 4; 4 - 6 2 - 2 4; 3 6 - 9 7 9)

1、 Consider matrix A as a column vector and write it 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,
2、 The first line and the fourth line are exchanged without changing the rank of the matrix
1,1,-2,7,
-1,1,-6,6,
-1,-2,2,-9,
2,1,4,3,
2,4,4,9,
3、 Using elementary row transformation, the matrix is operated
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, add it to the third row, and add it to the fourth row; multiply the second row by - 1, and add it to the fifth row:
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,4,-4.5,
0,0,16,-18,
5、 Add the third line to the fourth line, and the fourth line to the fifth line
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,-16,
6、 Add - 4 times the fourth line to the fifth line:
1,1,-2,7,
0,2,-8,13,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
7、 First 1 / 2 times the second line, then subtract the first line:
1,0,2,0.5,
0,1,-4,6.5,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
8、 Subtract the second line from the third line
1,0,2,0.5,
0,1,0,6,
0,0,-4,0.5,
0,0,0,-4,
0,0,0,0,
9、 - 1 / 4 times the third line, - 1 / 4 times the fourth line:
1,0,2,0.5,
0,1,0,6,
0,0,1,-0.125,
0,0,0,1,
0,0,0,0,
10、 Double the third line to subtract the first line:
1,0,0,0.75,
0,1,0,6,
0,0,1,-0.125,
0,0,0,1,
0,0,0,0.
11、 After the matrix is transformed into a ladder matrix by elementary transformation, the number of non-zero rows is the rank of the matrix, so the rank is 4, because 4 = rank

The inverse matrix of elementary transformation is 1 1; 0 2 3; 1 1 0;

(A,E)=1 1 -1 1 0 00 2 3 0 1 01 -1 0 0 0 1r3-r11 1 -1 1 0 00 2 3 0 1 00 -2 1 -1 0 1r3+r21 1 -1 1 0 00 2 3 0 1 00 0 4 -1 1 1r3*(1/4),r1+r3,r2-3r31 1 0 3/4 1/4 1/40 2 0 3/4 1/4 -3/40 0 1 -1/4 1/4 1/4r2*(...