The life-saving grace, when Yongquan reported, the masters came to help me ~~

skyblue2222

Long story short,
When I used the Gaussian elimination method to solve the functions of homogeneous linear equations (note that they are homogeneous), I encountered a problem. First I assumed a non-homogeneous linear equations:

3x + 2y-3z = 5
4x-3y + 6z = 1
      x-z = 3

List him as a matrix:

3 2 -3 5

4 -3 6 1

1 0 -1 3

Then I call the Gaussian elimination function to get the correct answer:

1 0 0 1.3

0 1 0 -2

0 0 1 -1.7

But if the equation is:

3x + 2y-3z = 0
4x-3y + 6z = 0
      x-z = 0

Then, the solution will always be:

1 0 0 0

0 1 0 0

0 0 1 0

Then, no matter what the coefficients of x, y, z are, as long as the constant terms on the right side of the equal sign are 0, then they will always be:

1 0 0 0

0 1 0 0

0 0 1 0

what happened?

skyblue2222

In fact, I wrote the Gaussian elimination function like this, and reduced the combined matrix to the simplest form. Then take the last column as the solution for x, y, z.

菜鸟级高手

3x + 2y-3z = 0
4x-3y + 6z = 0
      x-z = 0

Then, the solution will always be:

1 0 0 0

0 1 0 0

0 0 1 0

Then, no matter what the coefficients of x, y, z are, as long as the constant terms on the right side of the equal sign are 0, then they will always be:

This shows that the system of equations is unsolvable
It is normal for ternary equations to have no solutions
This corresponds geometrically to three planes with no common points
That the intersection of two pairs is parallel

skyblue2222

No, I mean when my function encounters the following equations:

a1x + b1y + c2z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3

d1 = d2 = d3 = 0
When all zeros to the right of the equal sign
After transformation:
1 0 0 0

0 1 0 0

0 0 1 0
The fourth column, which is what I want, is all zeros anyway.

菜鸟级高手

After thinking about it, your function is right
Because at this time all three planes pass the origin
So the origin is the only solution to this equation

sea0205

haha higher algebra problem

sea0205

There are two cases for the solution of this system of equations (all zeros to the right of the equal sign):
1. There is a unique solution, which is the zero solution.
2. Infinite solutions include zero solutions.
Don't know, right?
lz can go check out the book on advanced algebra! !! !!

larphone

mark
Class today, come back tonight to help you write.

lklklk

I have the code set to solve linear algebra here, leave EMAIL, I will send it to you

larphone

3x + 2y-3z = 0
4x-3y + 6z = 0
x-z = 0
Would you like to find the solution? X = y = z = 0. Right !!!!!!