Find the general solution x1-x2 + x3-x4 = 11 2x1 + 2x2 + x3-x4 = - 1 X1 + x2 + 2x3 + X4 = - 6 brothers, Such as the title X1-X2+X3-X4=11 2X1+2X2+X3-X4=-1 X1+X2+2X3+X4=-6

Find the general solution x1-x2 + x3-x4 = 11 2x1 + 2x2 + x3-x4 = - 1 X1 + x2 + 2x3 + X4 = - 6 brothers, Such as the title X1-X2+X3-X4=11 2X1+2X2+X3-X4=-1 X1+X2+2X3+X4=-6

The question is simple
By subtracting 1 from 2, we get X1 + 3x2 = - 12
Using formula 1 and formula 3, we can get 2x1 + 3x3 = 5
Get the relationship between X1 and x2x3
Then we get the relation between X1 and X4 by Formula 1
Finally, we get X1 = n x2 = - 4-N / 3 X3 = 5 / 3 - (2 / 3) n X4 = (2 / 3) - 16 / 3

How to select the free unknowns of linear equations?
6 -2
The fundamental solution system of 0 0 is not - 1 / 3 1, but 1 - 3

The general selection method of free unknowns: first, transform the coefficient matrix into a row simplified ladder matrix by elementary row transformation. The column of the first non-zero element of the row corresponds to the constrained unknowns, and the rest of the unknowns are free unknowns

The basic solution system of homogeneous linear equations, how to assign value to the free unknown quantity
As shown in the figure, can there be multiple forms of assignment? For example, if I make X3 = 1, X4 = 0; X3 = 0, X4 = 1, is the result correct? According to what law is the assignment? According to my method and the method on the figure, the answer can not be found to have any relationship, can it be the basic solution?
Here's the picture

Yes, when there is a free variable, there is an infinite assignment method. What you say is a common assignment method. What is shown in the figure is that according to the characteristics of the expression, the assignment method corresponding to the basic solution system of the integer can be obtained. For the assignment of a free variable, as long as the assignment is a linearly independent vector, for example, x3x4 is a free variable, So (x 3 x 4) = (10) and (0 1) are independent, or (1-3) and (0 4) given on the graph are independent, or (2 4) and (1 8) can be taken, I can take them at will

In linear algebra, the system of homogeneous linear equations is solved with known fundamental solution system
Find a system of homogeneous linear equations, so that its basic solution system is (0,1,2,3) and (1,2,3,0)
(I can't type that symbol either. That's the general meaning,

I've never seen such a problem before. Given the basic solution system, there are many homogeneous linear equations. We can only find it in reverse and write the simplest one, but it seems that there is a problem and we can't find it