ok thanks bro
#help-13
surreal ember
dense relic
I’ll help you out there
surreal ember
🙂
cedar kilnBOT
Available help channel!
turbid isle
So I copied the question and made a scenario. I checked the answer and it says true but I got false. Can someone explain what I did wrong
idle sonnet
So I copied the question and made a scenario. I checked the answer and it says t...
the trace is when you sum the diagonal entries
surreal ember
hi
idle sonnet
surreal ember
<:JustAsk:371662163489718273>
here
the third question
do I divide by the total?
idle sonnet
do I divide by the total?
can you show your work
cedar kilnBOT
@surreal ember Has your question been resolved?
idle sonnet
no but bro I wanted the third questino!!!
Oh sorry, that’s the one about percent natural abundance right?
cedar kilnBOT
idle sonnet
Notice that the peaks look like 1:2:1 ratio
so from that, you can get that the isotopes are in roughly equal abundance
cedar kilnBOT
Available help channel!
open crest
Hi! I'm really confused as to why finding the inverse function with 2 different methods results in two answers with completely different signs, but I can't seem to find any mistakes that I've made. I'd really appreciate an explanation for what I possibly did wrong, or if this is normal, why?
grave ether
yeah wait they are the same thing
open crest
wouldn't one of them have to be -y though? for the answers to be the same
oh wait, the denominators would not be affected by a sign change
i think?
grave ether
I actually have no idea what an inverse function is but the two final answers are the same are they not
open crest
i'm having trouble wrapping my head around that
grave ether
for the first one, factorise out -1 for the numerator
then for the second one, factorise out -1 in the denominator
open crest
sorry fhsjf i still don't understand
wraith daggerBOT
open crest
ohhh that makes more sense!
my friend told me to multiply by -1 in earlier step to see and this is what i got too
thank you for the explanation!!
so they really are the same
alpine cloak
cedar kilnBOT
alpine cloak
.rotate
median holly
3 x 2^x +1 x 2^x
when do you take common
when its in addition or subtraction lol
converse of distributive law
alpine cloak
where is the 1 from
median holly
multiplying 1 by any number
does nothing
so i just wrote 2^x as
1 x 2^x
for better understanding
obsidian coral
alpine cloak
for better understanding
so then after that i
median holly
you take 2^x common
alpine cloak
whay do i do with it
alpine cloak
how do u take it common
alpine cloak
yes
median holly
yes
alpine cloak
snd 1 is rhe co efficient of the other
median holly
not x^2
alpine cloak
snd u add the co efficients
median holly
yes
alpine cloak
i mean 2^x
alpine cloak
ohh ok thx
latent shell
vivid sundial
Hello
drifting matrix
vivid sundial
one thing i know its not parallel thats for sure
<1, -1, 1> = <2,-1,1>
does not equal
idle sonnet
it might be useful to replace the parameter in one of them by k instead of t
vivid sundial
it might be useful to replace the parameter in one of them by k instead of t
yea i did that i called the first one t1 the other t2
then i set them equal to each other
so i get 1 + t = 1 + 2t2 | 2 - t1 = 1 - t2 | 1 + t1 = t2
now here im stuck i dont know what to do
idle sonnet
so i get 1 + t = 1 + 2t2 | 2 - t1 = 1 - t2 | 1 + t1 = t2
then you can solve them simultaneously and see if they lead to a contradiction
vivid sundial
what do you mean by that
like do you mean
i take the first equation and solve for t2
ill get t2 = 0 is that right
1 + t1 = 1 + 2t \\ 1 = 1+t2 \\ t2 = 0
so it dosent intersct
intersect *
<@&286206848099549185>
idle sonnet
ill get t2 = 0 is that right
how
vivid sundial
Oh sorry mb I thought I couldn’t ping members
idle sonnet
I’ll let you ping me
vivid sundial
Ty
idle sonnet
ill get t2 = 0 is that right
how did you get this
vivid sundial
1 + t1 = 1 + 2t \\\ 1 = 1+t2 \\\ t2 = 0
.
I can do that right because technically it’s t
idle sonnet
I can do that right because technically it’s t
No, they are different
vivid sundial
Oooh
So how do I solve them
Wait is it
The x + y = let’s say c and then 2x + 2y = c
I forgot what’s it called
You mean I have to systems of equations
@idle sonnet
cedar kilnBOT
@vivid sundial Has your question been resolved?
keen plover
cedar kilnBOT
keen plover
Why is this wrong
tropic oxide
try DNE? maybe they want you to say DNE...
like as written the sequence does approach infinity...
keen plover
But isn’t the right answer infinity?
cold briar
Yes, it is infinity.
royal loom
sort of
keen plover
I only have 3 attempts
neat dune
The instructions say to write DNE
royal loom
infinity isn't a number so technically the limit DNE
cold briar
,w Limit[(n^4 - 4)/(n^2 + n), n -> Infinity]
wraith daggerBOT
keen plover
Bruh
cold briar
maybe they want you to write DNE
royal loom
the limit does not exist however because it grows without bound
you can think of this as approaching infinity
yet infinity still is not a number so the limit DNE
tropic oxide
try DNE
cold briar
When you say the limit does not exist, it means that the limit is either infinity, or not defined.
-Quora (idk)
keen plover
Idk man
tropic oxide
try DNE !!!
royal loom
DNE
neat dune
infinity isn't a number so technically the limit DNE
AkShUaLlY infinity is a number in the extended real number line but I seriously doubt they're being taught about it here :p
keen plover
Nah we good
royal loom
isn't a real number*
royal loom
it's not
neat dune
the instructions say to write DNE :p
tropic oxide
it's a difference in convention
tropic oxide
Can y’all show me a way to work this one out
do you know the method of dividing out by the highest power
keen plover
Yes
But the thing is
This one is in a square root
With another number
So idk what to do in this scenario
keen plover
?
keen plover
My bad I have no idea what those codes mean
I’m on a phone
So uhh
@royal loom
What’s the rule that allows me to take it out
cedar kilnBOT
@keen plover Has your question been resolved?
slender quartz
Can someone please for the love of god explain this stupid rule Ive been losing it since physics
slender quartz
I know mathematically how to calculate cross product but I cannot figure out the direction of it if just given a picture and asked for it
tropic oxide
with the handshape that's shown there, the rule is to curl your 4 fingers in the direction of rotation from a to b, and then the thumb will point in the direction of a×b
i dont like that rule because it is kind of confusing specifically in this instance
slender quartz
Ok let me give a better version
to help me understand
is this better to use to explain?
tropic oxide
uh hold on i think i took a picture of it myself at some point let me look for it
slender quartz
Alr, just ping me whenever 🙏 I appreciate your time and effort
tropic oxide
are a and b both meant to be parallel to the page?
slender quartz
uh unsure i was just providing an example, here's something solid that's better
Ignore math, just at the bottom it tells the direction
so i'd have to twist my arm to get the thumb down right
thumb - u
v - index
omg
it's out
tropic oxide
yeah
it points towards us
admittedly, my handshape sometimes requires putting your hand in somewhat of an awkward position.
slender quartz
okok
could you provide me an example see if i get it right myself?
y'know nvm, you're probably busy helping other people out.
I'll google some questions and practice it, ty for the trick!
.close
cedar kilnBOT
slender quartz
it's alright 😂 tysm
cedar kilnBOT
Available help channel!
harsh zephyr
hell
tropic oxide
30-60-90 triangle
vestal bear
cause thats it's value of the function
south tundra
Draw an equilateral triangle and a height from any point, you will have formed a right triangle where the acute angles are 30 and 60 degrees. You can solve for the length of the height using Pythagorean theorem and the fact that the height is also the median, hence you will know every trig-ratio of 30 and 60 degrees
harsh zephyr
Draw an equilateral triangle and a height from any point, you will have formed a...
ah thanks
i was confusing as to how we knew a 30-60-90 had those exact side lengths
.close
civic coral
given event A and B, why does A*B represents the
intersection of these two events
crimson sedge
product $\approx$ multiplication
wraith daggerBOT
Replaced by new brandon H
crimson sedge
Are you given two events or the probability of two events?
civic coral
just two events
cedar kilnBOT
@civic coral Has your question been resolved?
cedar kilnBOT
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Available help channel!
sullen raft
Hello, can someone help me find the angle(AMC)
cedar kilnBOT
Hello, can someone help me find the angle(AMC)
sullen raft
abc right triangle, ab = 12, bc = 24, m is the mid point of bc, so, BM=MC
sullen raft
No, I don't really know
neat dune
Hmm ngl that was the only way I've come up with so far 
sullen raft
does it have another name, or, is a specific formula, maybe the english name is not familiar with me
neat dune
What about law of cosines
sullen raft
a^2 = b^2 + c^2 - 2bc cos a?
neat dune
yeah but actually I came up with a way to do it without that
sullen raft
hmm
neat dune
OK now looking only at the lengths of triangle ABC you should be able to find the angle of C
neat dune
Do u know about 30-60-90 and 45-45-90 triangles?
sullen raft
ooh
not really
Actually
I think
180 is the sum
So I think I know what u mean
we have N 90
I'm a bit confused
:))
neat dune
lyeah but like they have certain memorable ratios to their sides
So like for instance 45-45-90 triangles have 1:1:sqrt(2) ratios
sullen raft
Um, I never heard of this
neat dune
Sigh gotta come up with a new way brb
sullen raft
:)))
I'm so sorry :))
it should be something easy... It's a book with not difficult problems, I know all the theory I did in school, I think it should be something different by that, since I don't know about circumradius use here or 45 45 90 ratio
neat dune
hm kinda surprised u know law of cosines but not these cus that's usually more advanced 
sullen raft
I know law of cosines bc I searched on internet like a week ago
and I memorized it
I have a pretty good memory, ngl
sullen raft
yea, until 60*
neat dune
Bet
sullen raft
sin of 30 is 1/2
I'm saying that only till 60
cuz in highschool is studied
90, 120
things like that
in our country
neat dune
OK so back to what we were doing previously which we can now do cus u know trig 😄
neat dune
Notice that 12/24 = 1/2.remind u of anything?
sullen raft
hmm
neat dune
Think of a trig value
neat dune
Could also be sin, and that would be preferable tbh since we're looking for the angle of C rn
so sinC =? In terms of the known lengths of ABC?
neat dune
Ye
sullen raft
that s what u've told earlier
neat dune
🙂
neat dune
Yup!
sullen raft
ooh
good
I love math
when someone explains it
good
we have c
and we were looking for
m
sullen raft
M would be 60
neat dune
Well just <NMC
neat dune
Ye so now we have part of <AMC. Now we gotta find <AMN
neat dune
Oh right lol I was tryna figure out a thing I forgot
OK so next up what's NC?
U have the hypoteneuse and <C
So set up some more trig
And solve for NC this time
Hypoteneuse is MC
neat dune
Because eventually it helps us find <AMN
neat dune
Triiiiig
Set up a ratio equal to some trig function that takes in <C as input
Like opposite/Hypoteneuse or adjacent/hypoteneuse
sullen raft
um
neat dune
lol
sullen raft
I know, yes
AMB with NMC?
or
wait
we don't have another triangle
to know length and an angle
sullen raft
oh, abc and nmc
neat dune
Ye
neat dune
Actually the nice thing here is that unlike what I was thinking of earlier we don't have to find any numerical values
I mean u still gotta write out ratios tho
neat dune
Well we know BC/MC
I guess you do have to calculate that numerical value :p
Soo uh calculate that
sullen raft
um
I am so confused now
I feel like an idiot
I think I'm an idiot
why there isn't a simple way
neat dune
lol
neat dune
We can do it
neat dune
Eh if u want I can just tell u the rest real quick
neat dune
BC/MC = 24/12 = 2 so AC = 2NC so AN = AC - NC = 2NC - NC = NC
Theeeen
Congruent triangles
AN = NC, MN = MN, right angle in between. SAS congruency
Finally <AMN = <NMC cus congruent triangles
So all of angle <BMC is 60 + 60 = 120
sullen raft
I think I'll deal with it a bit later, thank you so much!
do you have 'nother 5 mins
for an equation ?
neat dune
Ok
neat dune
Is it asking to evaluate a and then evaluate b separately?
neat dune
Kool
neat dune
Hmmm
Well as long as u know algebra the first set of para theses on a isn't too hard
Just add them like u would with fractions
Find common denominator and stuff
neat dune
For the second set of parentheses
It helps to factor
The values inside first
So 75 = 5^2*3 for instance
sullen raft
hmm
Aight, I will see
thank you so much, hope you'll have a nice day ! :)
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
lapis totem
How do I solve for Y? I need this for a graded assignment.
cedar kilnBOT
How do I solve for Y? I need this for a graded assignment.
tropic oxide
do you know trig
lapis totem
yeah
kinda
ive been learning for a week now but its still unclear to me
heres a better pic of the diagram
proven thistle
Wassup
lapis totem
yo
proven thistle
What do you need help with
lapis totem
i need to solve for Y
lapis totem
O = 93.34
P = 71.5
the problem is that i did a similar version to this problem and both have different valued outcomes of Y
hello?
you there?
guh
cedar kilnBOT
@lapis totem Has your question been resolved?
main herald
cedar kilnBOT
main herald
For this question am I doing 7 +7+x
Which then equals 14x
Could someone help me please
cedar kilnBOT
@main herald Has your question been resolved?
cedar kilnBOT
@main herald Has your question been resolved?
main herald
.close
crimson sedge
In how many different ways can eleven people be seated at a circular table with eight seats, if three are left waiting?
crimson sedge
This is a simplified version I did: (k-1)! (n) gave me the answer
or C(11,8)(8-1)!
(11!/8!3!) x 7!
The logic seems correct. Choose 8 people out of 11 people to occupy 8 seats. Then apply circular permutation on those people seated on those 8 seats.
,w (11 choose 8)*(7!)
wraith daggerBOT
cloud fiber
Could someone explain to me how definite integrals work with substitution example: x/x^2*8 dy/dx
crimson sedge
Could you please try to typeset the expression on latex bot?
cloud fiber
what is latex bot
crimson sedge
$\frac{x}{x^{2×8}} \frac{dy}{dx}$
wraith daggerBOT
- Miles12345
crimson sedge
Is this your expression?
cloud fiber
no 8 in the exponent
crimson sedge
$\left(\frac{x}{x^{2}}\right)^8 \frac{dy}{dx}$
cloud fiber
yes
wraith daggerBOT
- Miles12345
cloud fiber
definite integral from 0 to 5
dim tiger
there is no meaning for dy/dx here
cloud fiber
im sorry. I'm not very good at calculus
dim tiger
so there is no meaning to this $\int_{0}^{5}{(\frac{x}{x^2})^8}{\frac{dy}{dx}}$
wraith daggerBOT
calculus is fun
dim tiger
do you mean to type this $\int_{0}^{5}{(\frac{x}{x^2})^8}{dx}$
wraith daggerBOT
calculus is fun
dim tiger
now this makes sense
this doesnt require substitution
$\int_{0}^{5}{(\frac{x}{x^2})^8}{dx}=\int_{0}^{5}{(\frac{1}{x})^8}{dx}=\int_{0}^{5}{x^{-8}}{dx}$
wraith daggerBOT
calculus is fun
crimson sedge
dim tiger
now use what you know about $\int{x^n}dx$ $\forall x \in \mathbb{R}$
wraith daggerBOT
calculus is fun
crimson sedge
I don't intend to complicate things, but you can assume 1/x⁸ and dy/dx as two seperate functions and apply integration by parts:
(assuming you are integrating w.r.t. dx):
$\int\left(\frac{x}{x^{2}}\right)^8 \frac{dy}{dx}dx$
$ = \frac{1}{x^8}\int\frac{dy}{dx}dx - \int y \left(\frac{x^{-7}}{-7}\right) dx$
$ = \frac{y}{x^8} + \frac{1}{7} \int\frac{y}{x⁷} dx$
For that, you need to know what y is as a function of x. This is not substitution.
dim tiger
you forgot a dx in the first integral
crimson sedge
Oh yes thanks for pointing out
wraith daggerBOT
- Miles12345
dim tiger
yea
i didnt consider dy/dx bc we dont know abt y
and we dont have an integral or a differential equation to get y(if an explicit solution can be found even if there is a diff or int eq)
crimson sedge
To the OP
https://math.stackexchange.com/a/2396916
This comment shows how the integrating by substitution is derived (for indefinite integration, you can apply this for definite integration further by changing the integrating limits when substituting then using FTC1 in the end). This could clear up your concept about this
cedar kilnBOT
@cloud fiber Has your question been resolved?
crimson sedge
dire geode
!onechannel
cedar kilnBOT
Please stick to your channel.
dire geode
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
austere plume
What type of integration would I use for this
cedar kilnBOT
What type of integration would I use for this
foggy merlin
which one
austere plume
M
austere plume
Ok
How do I know I would use that
Instead of substitution by parts?
Since I can’t really tell when to use which
foggy merlin
Instead of substitution by parts?
substitution by parts ? what is this ?
foggy merlin
How do I know I would use that
Intuition
austere plume
substitution by parts ? what is this ?
When u use the formula uv-intergral sign V dy/dx
foggy merlin
its called integration by parts
austere plume
its called integration by parts
Yea that
My school calls it the other way
.closs
.close
shrewd gale
I need help, arithmetic
cedar kilnBOT
I need help, arithmetic
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
orchid summit
Do u know arithmetic progressions?
shrewd gale
This is my current progress
shrewd gale
Do u know arithmetic progressions?
Yes
orchid summit
Woah that was not ehat I was thinking
shrewd gale
okay
it's my first time coming across with arithmetic square roots
So I don't have an earthly idea how to solve this
orchid summit
I was thinking like difference between 36√3 and 8√3 is 28√3 (36√3 - 8√3 = 28√3).
orchid summit
im not sure if im correct and dont wanna give the answer out by mistake :(
orchid summit
Why wouldnt d be an irrational number? Whats so scary about that
oh thats a d 💀
i thought that was a reverse 6 and got confused 😭
shrewd gale
💀
orchid summit
yeah go on and find "d"
dense socket
Well you have an equation with one unknowm
How do you solve that
So...
It wasnt rly supposed to be a rethorical question
floral terrace
Ah hello there @shrewd gale haha
floral terrace
Square roots are basically like constants. you can treat them like "x" in some way.
floral terrace
So if you had something like $2\sqrt{3} + 3\sqrt{3}$, you can treat this as \ $2x + 3x$.
wraith daggerBOT
HqppyFeet
shrewd gale
AHH I get it
floral terrace
They have the same 3 the same applies in fraction right copy it?
exactly. They can be added/subtracted together because they have the same square root of 3
shrewd gale
Okayy you explain it so good
orchid summit
is thr a document which explains how to use TeXit 🤣
I wanna see so I can help explain a better way
floral terrace
https://atomurl.net/math/ this website taught me everything with Tex xD
orchid summit
alr thx xD
floral terrace
anyway- ye u got the idea fundora?
orchid summit
I knew how to explain it but saying root 3 = x sounds stupid 💀
dense socket
Nah its a good idea
floral terrace
yeah I know how that feels, I just call it sqrt(3), at least you understand that sqrt is square root
dense socket
I give that advice too
shrewd gale
dense socket
Cuz 2x + 3x Works the same way as 2 *sqrt(3) + 3 sqrt(3) but People get afraid of the sqrt part
Youre on right track fundora
Almost done
shrewd gale
Thanks
floral terrace
yess fundora! continue
orchid summit
Ur almost done 👀 nice
shrewd gale
I think it's done I was finding the common difference, Im gonna find a2 a3 a4
floral terrace
There ya go! 7sqrt(3) is your d.
shrewd gale
7 is the common difference I tried it out and it worked and got all the way up to 36
floral terrace
yess!!! I knew u could do it 🥹
shrewd gale
cedar kilnBOT
@shrewd gale Has your question been resolved?
verbal pawn
How do you solve this
cedar kilnBOT
How do you solve this
verbal pawn
I just took a quiz and I had literally no idea how to solve that
I’m in my car bombarded
orchid summit
Do u know what a square root is?
floral terrace
hmm, let's see.
what can 75 be factored to? Or what numbers multiply together to get 75?
orchid summit
hmm, let's see.
what can 75 be factored to? Or what numbers multiply together to...
Stop stealing my channel, ugh, I’m going u do it on ur own now 
orchid summit
What will it be
floral terrace
Stop stealing my channel, ugh, I’m going u do it on ur own now <:sully:651816820...
xDDD im sorzy
orchid summit
verbal pawn
hahaha
verbal pawn
okay
orchid summit
so 75 = 3 * 5 * 5
verbal pawn
yea
orchid summit
Now you know what a square is right?
orchid summit
yeah that 😭
Ok so now thinking about that we can say that √75 = √ 3* (5^2)
right?
proven radish
I need help asap what’s the name of the topics in these questions
orchid summit
I need help asap what’s the name of the topics in these questions
!help
cedar kilnBOT
I need help asap what’s the name of the topics in these questions
Please read #❓how-to-get-help
orchid summit
whr did u go man
orchid summit
YES
verbal pawn
5 the symbol 3
verbal pawn
dang
that’s a weird problem we didn’t even get it in homework or anything and it was on the quiz
thanks
U can close
orchid summit
that’s a weird problem we didn’t even get it in homework or anything and it was ...
Ur not done
Don’t u dare close
verbal pawn
Wtf
orchid summit
lol
verbal pawn
what do u mean I’m not done
verbal pawn
-25 symbol 3
orchid summit
@floral terrace || ngl when I saw the square shape I felt happy for the first time today ||
orchid summit
-25 symbol 3
Yep ur done
verbal pawn
U do it
thick portal
cedar kilnBOT
thick portal
so would x^2 cancel you the sqr from x-4
since your plugging in g(x) function for f(x)?
so it'll be f(x)=(sqrx-4)^2-5
hello?
.close
lime gyro
Help I dont know why my answer was incorrect
cedar kilnBOT
Help I dont know why my answer was incorrect
lime gyro
i was about to say lol
royal loom
!noclopen
cedar kilnBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem, and is confusing for helpers, making it more difficult for them to answer your question. We ask you to please be patient, even if your channel has not received much attention. If you are having a problem with a helper, please report it to <@&833154869451292722> rather than closing the channel and attempting to seek out another helper.
digital cliff
were you asked to do it by first principles? seems like a random way to do it
lime gyro
were you asked to do it by first principles? seems like a random way to do it
im assuming, its my first introduction to derivatives so i assume thats a yes
digital cliff
so you had [9h/(h-1)]/h
the issue is the next step
when you cancel that h it should become 9/(h-1) rather than 8h/(h-1)
if you carry on from there with that correction you should be fine
cedar kilnBOT
cosmic quiver
jade creek
ok
royal loom
they have their own open channel already. this channel is going to close, if you read the message sent by the bot
use #help-8
there is no reason to make this so difficult
jade creek
they have their own open channel already. this channel is going to close, if you...
ur good
you can go back now
cedar kilnBOT
Available help channel!
safe gate
Am I crazy, or would I need the mass of the block to be able to solve this?
safe gate
This is the only info provided.
<@&286206848099549185>
I tried combining F=ma with the equation for static friction, but that still brings up the problem that mass is not given.
muted bear
It would be n8ce if we can see the figure
digital cliff
its possible the mass, m, can be cancelled once you set everything up
broken ferry
hello
muted bear
What is fig 6.3.1
safe gate
muted bear
Have you drawn free body diagrams?
safe gate
Have you drawn free body diagrams?
with one force? I think the correct answer is to cancel M, this is a brand new problem type for me.
digital cliff
there would be 4 but only 2 that really matter
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
i need help with this, idk how to do piecewise functions
wraith daggerBOT
quadrangle
crimson sedge
not sure
-4 to -1
oh wait would it be -4 to 3
filled out 1 of them
5/3
2
3
got it
problem is idk how ud get the 4 from
how
crimson sedge
wait so how did u get the 4
yeah
-1?
3
there
final 2
3
4
figured it out
also
how do i do this version
-1?
wraith daggerBOT
quadrangle
wraith daggerBOT
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wraith daggerBOT
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cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
can someone help me with this?
crimson sedge
.close
shrewd violet
cedar kilnBOT
shrewd violet
can someone help me for b30 for span
buoyant latch
Consider a vector (x, y) ∈ ℝ²
Show that there exists an a, b ∈ ℝ such that a(2, 1) + b(1, 3) = (x, y)
For all (x, y)
shrewd violet
Show that there exists an a, b ∈ ℝ such that a(2, 1) + b(1, 3) = (x, y)
so solve for a?
buoyant latch
Not solve
buoyant latch
Show that there exists an a, b ∈ ℝ such that a(2, 1) + b(1, 3) = (x, y)
Show there exists
buoyant latch
And not just for a
shrewd violet
a and b
there is an x and y
that you can get an a
and b from
so this would be R^2
buoyant latch
There you go
shrewd violet
or can i write it like
buoyant latch
You have shown that given any point in ℝ²
You can write it in a linear combination of the elements in B
You haven’t shown they are linearly independent though
But you know for sure they span ℝ²
(There’s another theorem that instantly gets you independence as well)
shrewd violet
You haven’t shown they are linearly independent though
yea ik
buoyant latch
You don’t need to do that
buoyant latch
This is enough
shrewd violet
for example in this question
trying to find the span
it is different than the one i did and its confusing to what the span is
since x = z , z = x and b is the only coeff in which there exists an x and y
how do you tell teh span of this
buoyant latch
The first element is just 2 of the second + 1 of the third
shrewd violet
The first element is just 2 of the second + 1 of the third
no?
its not a scalar multiple
this is a plane
buoyant latch
It’s a linear combination of the other ones
shrewd violet
It’s a linear combination of the other ones
hm?
the 2nd vector has coeff of 2 and third coeff of 1?
to equal the first?
buoyant latch
It’s also obviously a plane by the 2nd and 3rd elements being independent by inspection
Yeah
v₁ = 2v₂ + v₃
So the v’s aren’t linearly independent
shrewd violet
so how can you tell the span isnt R^3 algebraically
sometimes i dont notice that
like i solved for a b and c
b is the only independent coeff
buoyant latch
You see how X fixes A and B
shrewd violet
wdym by fixes
buoyant latch
Well it also fixes the A and B for Z
shrewd violet
Well it also fixes the A and B for Z
wdym by fixes 💀
buoyant latch
For all (x, y)
This part
But in ℝ³ we have for all (x, y, z)
But actually you find that this is not true
You can’t actually find A B C’s that make it true for all (x, y, z)
Namely because x and z are expressed by the same linear combination of A and B
So when x ≠ z, there doesn’t exist an A and B in ℝ such that they express x and z at the same time
So for example say I want to express (1, 2, 0) in a linear combination of elements in B
I get 2A + B = 1
I get 2A + B = 0
There does not exist an A, B in ℝ that make those 2 true at the same time
shrewd violet
You can’t actually find A B C’s that make it true for all (x, y, z)
so you cant find something like a = x+2y-z
wait
shrewd violet
Namely because x and z are expressed by the same linear combination of A and B
im cofnsued 💀
????
shrewd violet
buoyant latch
Ok anyway
buoyant latch
so you cant find something like a = x+2y-z
You’re a bit mistaken
We choose some arbitrary x y z then we find the a b c’s
shrewd violet
sorry i didnt understand what you were implying
yea
we find a b c to see if they equal some combination of x y and z
buoyant latch
We don’t need to find them
shrewd violet
to see if it spans in R^3
buoyant latch
We need to show if they exist
shrewd violet
yeah i meant doing what i did here for R^2
buoyant latch
There does not exist an A, B in ℝ that make those 2 true *at the same time*
Clearly you can see here they can’t exist
Well you can solve the system of linear equations
shrewd violet
So for example say I want to express (1, 2, 0) in a linear combination of elemen...
but how would I know what vector to choose
buoyant latch
But you will end up with 2 different expressions for the A and B
buoyant latch
but how would I know what vector to choose
Well I looked at your first 3 equations
I see oh x and z are represented the same way
shrewd violet
oh i seee
buoyant latch
So if I chose x ≠ z then it won’t work
shrewd violet
so its only r^2
buoyant latch
Nope
shrewd violet
how
buoyant latch
None of ℝ² lives in ℝ³
shrewd violet
so if its not r^3 then what is it??
buoyant latch
Elements of ℝ² have only 2 components
shrewd violet
y axis in r^3?
buoyant latch
And every element of ℝ³ has 3 components
So it’s not that the span is ℝ²
But rather it spans a subspace of ℝ³ of dimension 2
buoyant latch
Or it spans a 2 dimensional subspace of ℝ³
What
What axis
No one said anything about axis
Axis are arbitrary
shrewd violet
spans in x or y plane of suspace of r^3
buoyant latch
That makes no sense
shrewd violet
x and y plane
shrewd violet
That still makes no sense
like for example
span of [1,0],[-1,0]
my prof said the span is
x-axis in r^2
buoyant latch
Sure you can say that spans the x-y plane
shrewd violet
so in this cacse