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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 22:51:27
is the plus (x^2 + i) correct?
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ramonov
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:51:35
that says x^2+1
0
1
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:51:53
i^2+1=0
0
1
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null
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:53:29
it might help to remember the conjugate root theorem to understand where i got x^2+1 from. i being a zero implies -i being a zero, implies (x-i)(x+i)=x^2+1 being a factor.
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help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 22:55:00
I'm not accustomed with complex numbers yet, but about the exercise I'm sure it's like that
1
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 22:56:10
I couldn't interpret the graph in regards to division by 6
1
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null
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 22:56:37
ah, it states = 27
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:57:37
It does work if g is meant to be an integer polynomial with those conditions
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help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:58:01
but in the realm of real polynomials, there are certainly many g st g(0) isn't divisible by 6
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 22:58:30
when we take out the 0.5 we'd have 54 which is divisible
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 22:58:40
yes you would.
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help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 23:00:17
that doesn't discount the fact that 0.5(x-2)(x-3)^2(x^2+1) is a counterexample
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null
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:02:31
it wouldn't save the question if I said if we scale the polynomial, we expect to scale the value 6 aswell, no?
1
0
220,517,274,845,577,200
ramonov
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ℝamonov
false
205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:02:55
because instead of 0.5 we can use any arbitrary scaling
1
0
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null
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:03:14
so division by whole number would get lost definitely
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:03:25
or not?
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 23:04:07
This could be me but I can't really figure out what you're trying to say
0
1
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
329,749,386,315,956,200
Sneaky
12/23/2021 23:04:55
The simplest way to save the problem would be to say g has to be an integer polynomial, but I don't really like doing the "guess what the question is meant to say" thing
0
1
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:06:21
I had a fallacy
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:08:25
well then
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:08:49
seems like a dead end to me with having your counterexample, so I'll have to ask my tutor
1
0
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205,809
help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:09:06
I thank you for your help @Sneaky
1
0
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help-1
8e56f39d9d704e209d984c55ffabc3ac
332,164,791,143,759,900
tarık b.
12/23/2021 23:09:36
.close
1
0
320,090,412,012,404,740
Kubra
2061
Kubra
false
205,810
help-1
5e1c9660972744508d4374eef73167e6
760,358,915,925,475,300
Intrexa
01/31/2022 21:14:22
Hey, I'm stumped on lim(x->pi/2) for (cos^2 x)/(1-sin x). I've tried messing around with substituting identities, either I'm off base, or not seeing it, or w/e
1
0
null
null
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205,810
help-1
5e1c9660972744508d4374eef73167e6
760,358,915,925,475,300
Intrexa
01/31/2022 21:14:49
Any help for the answer is good, any insight into the intuition as to why it's the answer is what I'm looking for
1
0
null
null
null
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205,810
help-1
5e1c9660972744508d4374eef73167e6
186,109,587,366,215,680
Omegabet_
01/31/2022 21:15:18
Hint: Pythagorean identity
0
1
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null
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null
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205,810
help-1
5e1c9660972744508d4374eef73167e6
760,358,915,925,475,300
Intrexa
01/31/2022 21:16:05
I tried throwing that in, (cos^2 x)/(cos^2 x + sin^2 x - sin x), but I'm stumped on that front
1
0
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null
null
null
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205,810
help-1
5e1c9660972744508d4374eef73167e6
186,109,587,366,215,680
Omegabet_
01/31/2022 21:16:18
$\cos^2(x)=1-\sin^2(x)$
0
1
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205,810
help-1
5e1c9660972744508d4374eef73167e6
510,789,298,321,096,700
TeXit
01/31/2022 21:16:20
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
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help-1
5e1c9660972744508d4374eef73167e6
760,358,915,925,475,300
Intrexa
01/31/2022 21:16:48
ahhh yeah
1
0
320,090,412,012,404,740
Kubra
2061
Kubra
false
205,810
help-1
5e1c9660972744508d4374eef73167e6
308,723,121,744,248,800
noot noot
01/31/2022 21:17:54
thanks pythagoras
0
1
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help-1
5e1c9660972744508d4374eef73167e6
760,358,915,925,475,300
Intrexa
01/31/2022 21:17:57
.close
1
0
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null
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help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
760,358,915,925,475,300
Intrexa
01/31/2022 21:18:02
thx all
1
0
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help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:11:26
how do i understand what {u, v} is because i set up the equations but don't know how they are equal to {u, v}
https://cdn.discordapp.c…0276/unknown.png
unknown.png
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:12:24
wdym?
0
1
320,090,412,012,404,740
Kubra
2061
Kubra
false
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:12:53
i don't know how to set up the system of equations
0
1
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null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:14:35
ok so lets do the first one together
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:15:11
we want to see if there are numbers (scalars) a,b such that a*[1,-2] + b * [-2,5] = [-2,5] correct?
0
1
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null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:15:30
yeah
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:15:58
ok, so then we simplify the LHS
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:16:14
we have [a-2a] + [-2b+5b] = [-2,5]
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:16:26
which implies that a-2b = -2, -2a+5b = 5
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:16:28
with me so far?
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:16:51
we then solve this system of linear equations
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:16:58
(which im assuming you know how to do)
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:18:16
ohh i think i understand how you made the system
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:18:20
yup
0
1
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null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:18:35
because [a,b] + [c,d] = [a+c, b+d]
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:19:41
ok then you can prove its a linear combination by finding a and b?
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:33:01
is the vector a linear combination of {u,v}? i solved the system of equations and got a=0 and b=1
0
1
null
null
null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:33:15
great
0
1
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null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:33:20
yup
0
1
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null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:34:22
since the A vector is similar to C is it also a correct linear combination?
0
1
null
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null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:34:47
what do you mean "similar"
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:34:58
but to answer your question, you did prove that it is a linear combination
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:35:34
they are both equal to the given vectors u and v
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:35:56
i dont see what you mean
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:36:01
plz give an example
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:36:36
https://cdn.discordapp.c…8807/unknown.png
unknown.png
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:36:36
https://cdn.discordapp.c…0628/unknown.png
unknown.png
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:36:36
https://cdn.discordapp.c…2752/unknown.png
unknown.png
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:37:12
correct
0
1
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null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:38:33
are those the only linear combinations in the list?
https://cdn.discordapp.c…4664/unknown.png
unknown.png
0
1
null
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null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:38:44
that is for you to figure out
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:38:47
repeat the process
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:38:48
😉
0
1
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:39:21
is it only a linear comb if there's a solution to the system
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:39:41
well yes
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:39:47
like if u = v = [0,0]
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:40:07
then if answer H is "The vector [1,1] is a lin. comb. of {u,v}
0
1
null
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null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:40:09
it is false
0
1
null
null
null
null
null
205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
714,316,705,303,625,900
Invictus
01/31/2022 22:40:11
get it?
0
1
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null
null
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:40:52
ohh ok then this probably means all real vectors are linear combinations
0
1
null
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205,811
help-1
5a7aec2de37a4a9588e6f74e2ca31bd1
315,292,317,315,629,060
Ptolemy
01/31/2022 22:48:17
@Invictus is choosing every vector that's not a multiple of u1 and u2 a good strategy to tell what's not in the span?
https://cdn.discordapp.c…6158/unknown.png
unknown.png
0
1
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null
null
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205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:16:13
the one sheeted hyperboloid has cartesian eqn:
1
0
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null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:16:40
x^2/a^2 + y^2/b^2 - z^2/c^2 = 1
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:16:51
what do a b c represent here
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:17:05
geometrically speaking!
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:17:09
lol
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:19:12
@Helpers
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
551,269,104,800,104,450
EndTimes
01/31/2022 23:44:22
@Helpers
1
0
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
569,167,697,925,898,240
Camilleone
02/01/2022 00:24:04
geometrically they're the principal semi-axes
0
1
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
183,668,144,404,037,630
Ann
02/01/2022 00:51:08
@EndTimes the 'unit' hyperboloid of one sheet has equation x^2 + y^2 - z^2 = 1
0
1
null
null
null
null
null
205,812
help-1
23adb9c9ea384313bf6c80dbb3393f7a
183,668,144,404,037,630
Ann
02/01/2022 00:51:22
dilating it by a, b and c along the x, y and z axes gives yours
0
1
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:27:44
Hey Guys, I have a problem with the calculation I have to get x1, x2 and x3 and it uses ZZ7, so Im not sure how to solve it, I used the gauss algorithm already, but I dont know whether its correct or not:
https://cdn.discordapp.c…6182/unknown.png
unknown.png
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:27:44
Hey Guys, I have a problem with the calculation I have to get x1, x2 and x3 and it uses ZZ7, so Im not sure how to solve it, I used the gauss algorithm already, but I dont know whether its correct or not:
https://cdn.discordapp.c…0592/unknown.png
unknown.png
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:28:17
Also, I got out for x1 = 1.5, for x2 =0 and for x3 = -1
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:29:34
Or was I wrong to use the Gauss Algorithm here?
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
510,789,298,321,096,700
TeXit
02/01/2022 02:32:50
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
706,934,233,012,371,600
Ansh_
02/01/2022 02:33:17
hmm the Z7
0
1
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:33:45
Well, I was a bit confused because I'm limited to the body ZZ7 right? This one
https://cdn.discordapp.c…9578/unknown.png
unknown.png
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:34:16
Or maybe its called a "field" in english
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:34:35
So the number only goes from 0 up to 6
1
0
320,090,412,012,404,740
Kubra
2061
Kubra
false
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:34:42
(I think)
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 02:41:53
yup
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 03:42:42
Well, if no one knows the answer to those, I would need help with something else as well
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 03:43:18
Give the generator polynomials and the corresponding generator matrices and control polynomials of all 6-digit cyclic codes with 3 control digits over Z5.
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
236,549,522,178,834,430
Revogue
02/01/2022 03:43:43
And I'm absolutely confused on how I can do that
1
0
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
915,938,343,857,037,300
Quincy
02/01/2022 04:05:27
If u know inverse matrix, then just multiply inverse of the 3*3 matrix to both the sides. The LHS become only x1,x2,x3 and RHS will be inv(3*3) matrix * (1,3,1) matrix
0
1
null
null
null
null
null
205,813
help-1
3cb2f7639f2549b1a75e0907763ac032
595,185,421,743,554,600
Sepdron
02/01/2022 04:27:27
i think i know how to do it, i think it's like gauss algorithm but instead of dividing, you multiply it by its multiplicative inverse in the finite field i think it helps if you make the multiplication table for the finite field first
0
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