Is this the simplest form of row ladder matrix? A=0 -2 1 0 0 0 3 0 -2 0 0 0 -2 3 0 0 0 0 It can be reduced to 0 - 21 100 0 0 0 0 -1 0 0 0 0 0 0 1 Can continue to be transformed into 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 or 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 According to the definition of row ladder minimalist matrix: all the elements under the ladder are 0, and the number of steps is the number of non-zero rows. The first element behind the vertical line of the ladder is non-zero, which is also the first non-zero element of the non-zero row, and all other elements in its column are 0. * * * the row minimalist matrix of a matrix is uniquely determined*** All the above matrices meet the above definition, but the asterisk says that the only way to be sure is to have only one. Why? Is it not the simplest form if it can be simplified again? But the simplest answer is: 1 0 0 6 3 4 0 1 0 4 2 3 0 0 1 9 4 6 If 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 In the simplest form, isn't that a contradiction? ***If we want to change it into the simplest form of row, we must only carry out "row elementary transformation" instead of "column elementary transformation"? *** Thank you for your serious answer. If you have the Tongji version 4, you can see that the last element in line 2 of p61 example 1 is indeed - 2

Is this the simplest form of row ladder matrix? A=0 -2 1 0 0 0 3 0 -2 0 0 0 -2 3 0 0 0 0 It can be reduced to 0 - 21 100 0 0 0 0 -1 0 0 0 0 0 0 1 Can continue to be transformed into 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 or 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 According to the definition of row ladder minimalist matrix: all the elements under the ladder are 0, and the number of steps is the number of non-zero rows. The first element behind the vertical line of the ladder is non-zero, which is also the first non-zero element of the non-zero row, and all other elements in its column are 0. * * * the row minimalist matrix of a matrix is uniquely determined*** All the above matrices meet the above definition, but the asterisk says that the only way to be sure is to have only one. Why? Is it not the simplest form if it can be simplified again? But the simplest answer is: 1 0 0 6 3 4 0 1 0 4 2 3 0 0 1 9 4 6 If 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 In the simplest form, isn't that a contradiction? ***If we want to change it into the simplest form of row, we must only carry out "row elementary transformation" instead of "column elementary transformation"? *** Thank you for your serious answer. If you have the Tongji version 4, you can see that the last element in line 2 of p61 example 1 is indeed - 2

Elementary row transformation, you must be a column transformation. Column transformation generally only used when rank
If we want to simplify the row, we must only carry out "row elementary transformation" instead of "column elementary transformation"?
Linear algebra said, into the simplest line, can only carry on the elementary line transformation
My friend, your questions are all wrong
A = 0 - 21, reduce (a, e) to the simplest line
3 0 -2
-2 3 0
（A,E）=0 -2 1 1 0 0
3 0 -2 0 1 0
-2 3 0 0 0 1
r3*3
r3+2*r2
R1 and R2 are interchangeable
=3 0 -2 0 1 0
0 -2 1 1 0 0
0 9 -4 0 2 3
r3*2
r3+9*r2
= 3 0 -2 0 1 0
= 0 -2 1 1 0 0
= 0 0 1 9 4 6
r1+2*r3
r2-r3
=3 0 0 18 9 12
=0 -2 0 -8 -4 -6
=0 0 1 9 4 6
r1/3
r2/(-2)
=1 0 0 6 3 4
0 1 0 4 2 3
0 0 1 9 4 6
OK, done! Remember, the transformation can only use elementary row transformation, later you will know, the last matrix after the simplification is the inverse matrix of the given matrix! Ha ha
Tired to death~~~~
I missed the - 2. I mean, the topic should be simplified
(a, e) instead of (a, 0e), or no one can do it