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chrisplusian

  • one year ago

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

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  1. chrisplusian
    • one year ago
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  2. jango_IN_DTOWN
    • one year ago
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    no

  3. jango_IN_DTOWN
    • one year ago
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    you need to make the coefficients of the rhs 0 and then solve

  4. chrisplusian
    • one year ago
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    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

  5. chrisplusian
    • one year ago
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    What did you mean by the "rhs"? @jango_IN_DTOWN

  6. anonymous
    • one year ago
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    right hand side

  7. chrisplusian
    • one year ago
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    Ok but isn't that what an associated homogeneous system is? When you make the rhs =0?

  8. anonymous
    • one year ago
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    you have to solve the augmented matrix, then you can find the general solution.

  9. chrisplusian
    • one year ago
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    Ok If you could look at the example I posted could you tell me if the "part ii" is correct for the general solution?

  10. chrisplusian
    • one year ago
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    @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?

  11. chrisplusian
    • one year ago
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    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

  12. jango_IN_DTOWN
    • one year ago
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    https://math.dartmouth.edu/archive/m8s00/public_html/handouts/matrices2/node8.html

  13. jango_IN_DTOWN
    • one year ago
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    go through this link

  14. jango_IN_DTOWN
    • one year ago
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    I am sure you will get what is required

  15. chrisplusian
    • one year ago
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    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.

  16. jango_IN_DTOWN
    • one year ago
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    ok no problem

  17. chrisplusian
    • one year ago
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    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.

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