Question

Linear algebra question..... Is a "general solution" to a system the same as a solution to the associated homogeneous system? (see attachment)

Answer 1

no

Answer 2

you need to make the coefficients of the rhs 0 and then solve

Answer 3

Did you see in the example we were given in a lecture hand out? Where I drew the line? That was the end of the explanation and it seemed like he was saying that was the solution to part two

Answer 4

What did you mean by the "rhs"? @jango_IN_DTOWN

Answer 5

right hand side

Answer 6

Ok but isn't that what an associated homogeneous system is? When you make the rhs =0?

Answer 7

you have to solve the augmented matrix, then you can find the general solution.

Answer 8

Ok If you could look at the example I posted could you tell me if the "part ii" is correct for the general solution?

Answer 9

@Lily2913 in the above example both "augmented" matrices are solved. There is one with a particular solution which says the system is inconsistent. Then they solve the associated homogeneous system for part ii. My problem is that in part ii they ask for a general solution. I am trying to make a conclusion from the example. Is the associated homogeneous solution the same as a "general solution"? Or is it only in this case because the particular solution gave an inconsistent system? If the first part would not have resulted in an inconsistent solution would the general solution have been different?

Answer 10

And @Lily2913 this came from my Professors, lecture handout. I am not sure where you were asking if I got it from, but Unless it is University of North Florida then no I didn't get it from there

Answer 11

https://math.dartmouth.edu/archive/m8s00/public_html/handouts/matrices2/node8.html

Answer 12

go through this link

Answer 13

I am sure you will get what is required

Answer 14

I am sorry, I just realized that I started reading one side of my notes, and after my son walked in to ask me a question I started reading a different side of the notes and confused the issue. SO I will try again reading the same side... I apologize. If I am still confused I will repost a sensible question.

Answer 15

ok no problem

Answer 16

Yeah I went back and looked at the correct side, and followed the link you gave me, but I still don't understand. The webpage explains in terms of differential equations, and I took that class over two years ago, so I can't remember that either.