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Thread: First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

  1. #101
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by InteGrand View Post
    What other method do you have in mind? (Induction helps takes care of it nicely if you want to prove it straight from the axioms.)

    For some reason I kept thinking what was the problem with doing it component wise...

    In that case, how could you prove this then?


    As a reference, they proved like this


    Also gonna take a stab at the axioms they used...
    1. Existence of 0
    2. Scaling factor of 1
    3. arithmetic (or just existence of 0 in field of scalars)
    4. Scalar distributive law
    5. Scaling factor of 1
    Last edited by leehuan; 23 Aug 2016 at 10:12 AM.

  2. #102
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    For some reason I kept thinking what was the problem with doing it component wise...

    In that case, how could you prove this then?


    As a reference, they proved like this


    Also gonna take a stab at the axioms they used...
    1. Existence of 0
    2. Scaling factor of 1
    3. arithmetic (or just existence of 0 in field of scalars)
    4. Scalar distributive law
    5. Scaling factor of 1




    We can't just do these component-wise because they are results about arbitrary vector spaces (not necessarily ones where the vectors are n-tuples).
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  3. #103
    Kosovo is Serbian RenegadeMx's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    For some reason I kept thinking what was the problem with doing it component wise...

    In that case, how could you prove this then?


    As a reference, they proved like this


    Also gonna take a stab at the axioms they used...
    1. Existence of 0
    2. Scaling factor of 1
    3. arithmetic (or just existence of 0 in field of scalars)
    4. Scalar distributive law
    5. Scaling factor of 1
    man i feel sorry if they expect u to properly remember the axioms, for us we just had to use 2 or 3.



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  4. #104
    Supreme Member seanieg89's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    They really aren't hard to remember.

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by seanieg89 View Post
    They really aren't hard to remember.
    annoying as fuck tho



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  6. #106
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    The axioms are just annoying.

    Actually knowing when and how to use them like there though is ...

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    Supreme Member Flop21's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    S = {x is an element of R^4 | (x1)-5(x3) = 2(x4)}


    Find one non-zero element in S.


    Do you just sub in random values for x1,x3,x4 (also where's x2)?
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    S = {x is an element of R^4 | (x1)-5(x3) = 2(x4)}


    Find one non-zero element in S.


    Do you just sub in random values for x1,x3,x4 (also where's x2)?
    x=(2,0,0,1) x2 can be whatever u want doesnt affect the eqn



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  9. #109
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Don't mind if this question isn't finished off for me but can someone please set it up? Finding it hard to set everything out neatly here.


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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Don't mind if this question isn't finished off for me but can someone please set it up? Finding it hard to set everything out neatly here.

    Is there missing detail like Ax = 0 or Ax is an element of ___

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    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by HeroicPandas View Post
    Is there missing detail like Ax = 0 or Ax is an element of ___
    Nope, and I know it can't be Ax=0 because that's a system of linear equations.

    Pretty sure by assumption Ax is an element of R3 if the whole set is a subspace of R3

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Nope, and I know it can't be Ax=0 because that's a system of linear equations.

    Pretty sure by assumption Ax is an element of R3 if the whole set is a subspace of R3
    Woops, I did a mistake in dimension and thought that Ax is still 3x5 matrix

  13. #113
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Don't mind if this question isn't finished off for me but can someone please set it up? Finding it hard to set everything out neatly here.

    i forgot the proper proof for these

    U is subset of r3 which is known v.s <- not sure if u need to include this for first year, but im used to writing it anyway..

    0 vector is obvious
    Ax+Ay=A(x+y) y element of U etc i.e A(0)+A(0)=A(0+0) = 0
    A*(Landa)(x)=(Landa) Ax landa is real, can be complex if u want A*Landa(0)-Landa A(0) =0
    Last edited by RenegadeMx; 25 Aug 2016 at 12:41 AM.
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    Quote Originally Posted by Shadowdude View Post
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  14. #114
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Don't mind if this question isn't finished off for me but can someone please set it up? Finding it hard to set everything out neatly here.





    Last edited by InteGrand; 25 Aug 2016 at 12:44 AM.
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    Re: MATH1231/1241/1251 SOS Thread

    In other words, to show a set S is closed under addition, it means we have to show that if a and b are arbitrary elements of S, then so is a+b.

    To show the set U is closed under scalar multiplication, it means we have to show that if c is an arbitrary scalar and v an arbitrary vector from U, then cv is also in U.
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    Re: MATH1231/1241/1251 SOS Thread

    heres another one where u need to think more carefully compared to the easy stuff like 3x1+2x3=0 (if u want the practice)




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  17. #117
    Supreme Member Flop21's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    For this polynomial question, I get the same matrix but R1 and R3 swapped. Is this still okay, or is my method wrong?

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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by Flop21 View Post
    For this polynomial question, I get the same matrix but R1 and R3 swapped. Is this still okay, or is my method wrong?

    As long as you have the same rows, you'll end up at the same answer (because then you're starting off with the same set of simultaneous equations, just written in a different order, which clearly won't affect the solutions).
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  19. #119
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by RenegadeMx View Post
    heres another one where u need to think more carefully compared to the easy stuff like 3x1+2x3=0 (if u want the practice)

    I'll go for it if I get the time

  20. #120
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    ^Feelsbad delaying the exercise

    Anyway



    Is this just because the zero polynomial can't be in S?

  21. #121
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    ^Feelsbad delaying the exercise

    Anyway



    Is this just because the zero polynomial can't be in S?
    yes
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  22. #122
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    Re: MATH1231/1241/1251 SOS Thread

    to prove its not a v.s in general u either show 0 isnt there (easiest) or that it doesnt satisfy addition/scalar multiplication

    only need to show 1 of those conditions as well
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    Quote Originally Posted by Shadowdude View Post
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    Quote Originally Posted by Shadowdude View Post
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  23. #123
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by RenegadeMx View Post
    yes
    Lol sweet.
    _______________________

    Even if there IS a typo in the notation, this question is actually confusing me to the maximum...



    This was the answer I got to part (ii)

    Last edited by leehuan; 25 Aug 2016 at 9:51 PM.

  24. #124
    Ancient Orator leehuan's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by RenegadeMx View Post
    to prove its not a v.s in general u either show 0 isnt there (easiest) or that it doesnt satisfy addition/scalar multiplication

    only need to show 1 of those conditions as well
    Yeah sweet, that reaffirms what I know

  25. #125
    -insert title here- Paradoxica's Avatar
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    Re: MATH1231/1241/1251 SOS Thread

    Quote Originally Posted by leehuan View Post
    Lol sweet.
    _______________________

    Even if there IS a typo in the notation, this question is actually confusing me to the maximum...



    This was the answer I got to part (ii)



    You forgot that α⁵=1
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    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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