Linear stuff: I never get the awnser

• cmab
In summary, the conversation is about solving two equations with four unknown variables. The speaker is confused about how to begin and has been getting answers that seem far from the actual answer. The expert explains that there are multiple ways to solve the equations and suggests using substitution. The expert then provides a step-by-step explanation and shows that the given answer and their solution are equivalent, with different parameter choices. The expert also mentions that there are 2 degrees of freedom in this problem and that the equations will depend on the choices made for the parameters.
cmab
Linear stuff: I never get the awnser...!

[3 1 1 1 0]
[5 -1 1 -1 0]

Where the variables are X1 X2 X3 X4.

I always get somethignt that is far away from the answer.
The answer should be x1= -s x2=-t-s x3=4s x4 = t

cmab said:
[3 1 1 1 0]
[5 -1 1 -1 0]

Where the variables are X1 X2 X3 X4.

I always get somethignt that is far away from the answer.
The answer should be x1= -s x2=-t-s x3=4s x4 = t

What did you do to begin?

apmcavoy said:
What did you do to begin?

At first, i putted the first number in the frist row as 1.

so i get [1 1/3 1/3 1/3 0]
than i eliminate the 5 to make it a 0.
But its after that i got ****ed!

mayday!

cmab said:
[3 1 1 1 0]
[5 -1 1 -1 0]

Where the variables are X1 X2 X3 X4.

I always get somethignt that is far away from the answer.
The answer should be x1= -s x2=-t-s x3=4s x4 = t

What was the question?? I think you have two equations in 4 unknowns and both equations are equal to 0. (It is mildly confusing that you tell us the variables are X1, X2, X3, X4 but then write x1, x2, x3, and x4!)

Do you understand that there are many different ways to write the answer depending on exactly how you do this? It might be that your answers that are "far away from the answer" are, in fact, exactly on the answer!

You could do this by "row reducing" but with a simple problem like this I think just "substitution" is best.

The equations are 3x1+ x2+ x3+ x4= 0 and 5x1- x2+ x3- x4= 0. I might do something like add the two equations and get 8x1+ 2x3= 0 so that x3= -4x1.
Now, I choose (arbitrarily) to make x1= s. Then x3= -4s. Putting those into the two equations I get 3s+ x2- 4x+ x4= 0 or x2+ x4= s and
5s- x2- 4s- x4= 0 or x2+ x4= s. Since those two equations are exactly the same, I choose (again arbitrarily) to let x2= t and solve for x4= s-t.
My solution is x1= s, x2= t, x3= -4s, x4= s-t.

Is that "far away from the answer", which was x1= -s x2=-t-s x3=4s x4 = t? No, not at all. It might make a little more sense if I don't use the same letters as in your given answer: In my answer use "u" instead of "s" and "v" instead of "t". Then my answer is x1= u, x2=v, x3=-4u, x4= u- v. Looking at the "given" answer, I see that x1=u= -s. If I just replace u by -s, I will have both x1= -s and x3= -4u= 4s as in the "given" answer. MY x2 was v while the "given" x2 is -t-s. That would be the same if v= -t-s. In that case, my x4= u- t would become x4= (-s)-(-t-s)= -s+ t+ s= t, exactly as given.

That means that the set of points from my answer and the "given" answer are exactly the same! For example, If you take s= 1, t= 1 in the "given" answer you get x1= -1, x2= -2, x3= 4, x4= 1.
If you take s= -1, v= -2 (in my original form. In terms of u, v, I am taking u= -s= -1, v= -t-s= -2.) so that x= s= -1, x2= t= -2, x3=-4s= 4, x4= s-t= 1, just as before.

Because there are 2 (independent) equations in 4 unknowns, we have 4-2= 2 "degrees of freedom". We are free to choose any two parameters, arbitrarily, and write x1, x2, x3, x4 in terms of those two parameters. Of course, the equations you get will depend upon those arbitrary choices.

Last edited by a moderator:
Thanks bud, i'll look at it later on. If i have any problem, i'll post.

1. What is linear stuff?

Linear stuff refers to a mathematical concept and method of analysis that involves studying relationships between variables that can be represented on a straight line. It is often used in fields such as physics, engineering, economics, and statistics.

2. How is linear stuff used in science?

In science, linear stuff is used to analyze and understand the relationships between different variables. This can help scientists make predictions, identify patterns, and draw conclusions about their research. Linear stuff is also used to create mathematical models that can be used to make predictions and test hypotheses.

3. What are the key components of linear stuff?

The key components of linear stuff include variables, equations, and graphs. Variables are the quantities that are being studied, equations describe the relationship between the variables, and graphs visually represent the relationship between the variables on a straight line.

4. What are some real-world applications of linear stuff?

Linear stuff has many real-world applications, including predicting future trends in data, analyzing the relationship between different factors, and creating mathematical models for solving real-world problems. It is used in fields such as economics, sociology, and environmental science.

5. Why do some people struggle to understand linear stuff?

Some people may struggle to understand linear stuff because it involves complex mathematical concepts and equations. It also requires a strong understanding of algebra and the ability to visualize relationships between variables on a graph. Practice and a solid foundation in math can help improve understanding of linear stuff.

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