In linear algebra, the basic analysis of solving the second linear equations X1 -8X2 -10X3 +2X4=0 2X1 +4X2 +5X3 -X4=0 3X1 +8X2 +6X3 -2X4=0 I know we need to use elementary transformation. I want an answer to this question The answer to this question is 1 = (0 1 04); (2 = (- 4 01 - 3), What I do is 1 = (- 4 - 3 10) 2 = (0 401) In the formation of elementary transformation, two rows can be interchanged, which two columns can be interchanged? I'm replacing your last step, the second column and the fourth column, with a minus sign.

In linear algebra, the basic analysis of solving the second linear equations X1 -8X2 -10X3 +2X4=0 2X1 +4X2 +5X3 -X4=0 3X1 +8X2 +6X3 -2X4=0 I know we need to use elementary transformation. I want an answer to this question The answer to this question is 1 = (0 1 04); (2 = (- 4 01 - 3), What I do is 1 = (- 4 - 3 10) 2 = (0 401) In the formation of elementary transformation, two rows can be interchanged, which two columns can be interchanged? I'm replacing your last step, the second column and the fourth column, with a minus sign.

You have written the title wrong. The first equation should be X1 & nbsp; - 8x2 & nbsp; + 10x3 & nbsp; + 2x4 = 0 & nbsp;
The number of vectors in the basic solution system of homogeneous linear equations is certain, but the expression of these vectors is not unique, so it is not necessarily wrong to be inconsistent with the answer;
The result you get is wrong, because section 1 = (- 4 & nbsp; - 3 & nbsp; 1 & nbsp; 0) section2 = (0 & nbsp; 4 & nbsp; 0 & nbsp; 1) is not the solution of the system of equations at all & nbsp;
The answer is to take x2 and X3 as free unknowns, and you may take X3 and X4 as free unknowns. There's no problem, but you made a mistake when seeking the basic solution system & nbsp;
The process is shown in the figure below. If you can't see it clearly, you can click to enlarge it
＝＝＝＝＝＝＝＝
Supplement:
If you change the two columns, will the equations change or not?
What is the relationship between elementary row transformation and solving equations? These should be explained in textbooks
Why do all the examples in the textbook use elementary line transformation?
.
In the final analysis, the method of solving equations is elimination method, which is expressed by row transformation of matrix
Therefore, only row transformation can be used

On the value of free unknowns in linear algebra
That's how it works out
x1=0
2x2+2x3=0
I took X3 as 1 and calculated it to be 0 1 - 1. In the book, I took X3 as 1
Is the result all right? This question is standardized
And that's why sometimes a free unknown is assigned to a letter like C

All right,
The letter C represents the free unknown as a general solution
Taking a specific value is the special solution of the general solution