💀
#help-39
formal tiger
rigid mist
,rccw
jolly parrotBOT
formal tiger
Idk what im doing man
misty nymph
no you cannot distribute the square like that on the left hand side
rigid mist
Danny is here, whats up man, long time no see
misty nymph
Danny is here, whats up man, long time no see
lol you might have me confused for someone else. i just joined this server like an hour ago
rigid mist
yup ik, how can you even forget about me?, we were frnds dude
okay enough, so @formal tiger
formal tiger
Hi
formal tiger
misty nymph
pearl pondBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
rigid mist
you could possibly be jailed for doing this
misty nymph
you know how you isolated the square root on one side and squared it?
just do that again
misty nymph
show me what you got so far
formal tiger
misty nymph
before you square it. move everything on the left side that isnt the square root to the right hand side.
but useing algebra
misty nymph
oh my bad. i misunderstood your handwritting lol
yeah so square both sides now
to get ride of the square root
formal tiger
Ok
I still got itbwrong
😭
The answer is 6
But idk how to get there
Waitt
NVM
I GOT IT
I FORGOT AB THE OTHER SIDE
YAYY THANK U DANNY
misty nymph
congratz
devout plinth
plz someone help me through this
pearl pondBOT
plz someone help me through this
devout plinth
i never learned something similar like this in class
spice snow
have you worked with the distance between two points?
devout plinth
have you worked with the distance between two points?
yes
we did distance and midpoint formula
spice snow
great
dapper kraken
isnt it just pythag
spice snow
so if we know that the distance between (0,n) and (5,0) is n+1, can we set up an equation to find n?
dapper kraken
nvm
spice snow
isnt it just pythag
yeah
devout plinth
so if we know that the distance between (0,n) and (5,0) is n+1, can we set up an...
in the form of distance formula?
spice snow
the distance formula should be equal to n+1, right?
devout plinth
yes
spice snow
so how could we set up an equation for that
devout plinth
d= square root of (5-0)^2 + (0-n)^2 ?
dapper kraken
what does the second point mean, "State another point that is the same distance from (5,0) that has x- coordinate 0"
spice snow
d= square root of (5-0)^2 + (0-n)^2 ?
that's the distance, but we also know that d=n+1
so we could say sqrt((5-0)^2 + (0-n)^2) = n+1
devout plinth
okay
spice snow
now we can answer the question ("find the value of n") by just solving for n
spice snow
d= square root of (5-0)^2 + (0-n)^2 ?
do write the general formula since the problem asks you to, too
spice snow
right, now we just need to solve for n
devout plinth
right, now we just need to solve for n
do i substitute the distance formula with n+1
im not sure how to solve for n this way
jolly parrotBOT
fede
devout plinth
okay
spice snow
how can we "reverse" the square root?
dapper kraken
if you make the swuare root.and reverse it it after without using it why would you make the square root in the first place?
devout plinth
how can we "reverse" the square root?
squaring it?
spice snow
if you make the swuare root.and reverse it it after without using it why would y...
because our goal here is to find the n that makes that distance formula give you n+1
jolly parrotBOT
fede
spice snow
i'm going to change a little thing before we move on
we know (-n)^2 = n^2, which will make things a bit easier
devout plinth
mhm
spice snow
so $5^{2}+n^{2} = (n+1)^{2}$
jolly parrotBOT
fede
spice snow
what would be the next step if we want to isolate n?
spice snow
hmm, check this
if we expand the terms on the right, we will get an n^2 on both sides
dapper kraken
after you do the next step
spice snow
and if we get an n^2 on both sides, we can substract them
so expanding the terms on the right seems to make the most sense
devout plinth
ohh ok so are we distributing the square?
devout plinth
5^2 + n^2 = n^2 + 1
jolly parrotBOT
fede
devout plinth
hm
spice snow
in this case a=n and b=1
devout plinth
righyt
dapper kraken
wanna know, what grade is this question?
spice snow
so what would the equation look like
spice snow
we are expanding (n+1)^2 to try to express it in another way that can help us find n easier
spice snow
**fede**
that is one way to do it! We will arrive at the same result as applying this formula
how do we expand that
devout plinth
wait so are we subsituting the contents for that formula
spice snow
we are expanding (n+1)^2
spice snow
**fede**
if a=n and b=1, we would get n^2 + 2*n*1 + 1^2
so we get n^2 + 2n + 1
does that make sense?
devout plinth
yes
spice snow
so in the end we have $5^2 + n^2 = n^2 + 2n + 1$
jolly parrotBOT
fede
spice snow
and if we get an n^2 on both sides, we can substract them
and here is where we can do what we said earlier
devout plinth
25
spice snow
so we have $25 = 2n+1$
jolly parrotBOT
fede
devout plinth
so n=12
spice snow
that's correct
devout plinth
wowzers
i had no idea i had to like
apply algebra formulas to geometry equations
spice snow
yeah! everything is connected
devout plinth
plz someone help me through this
how would i state the point now?
spice snow
if n=12, what is (0,n)
devout plinth
oh right
(0,12)
how would i do the last part of the question ?
where i have to state another point
spice snow
the wording is a bit unclear to me.. let me try to understand what we have to do here
devout plinth
okk
spice snow
OHHH i got it
okay
so we know that if the x coordinate is 0, the point will look like (0,y) right?
devout plinth
yes
spice snow
and the distance to (5,0) is the same, n+1. since n=12, the distance must be 13
so $\sqrt{5^2+y^2} = 13$
jolly parrotBOT
fede
devout plinth
ok
question why are we squaring the y
is it because the coordinates are x^2 and y^2
spice snow
i simplified it a bit, it's (y-0)^2
devout plinth
oh ok i got u
spice snow
since we have (5,0) and (0,y)
okay so, like we did earlier, we square to remove the square root
so we get?
devout plinth
5^2+y^2 = 13^2 ?
jolly parrotBOT
Result:
169
$y^2 + 25 = 169$
jolly parrotBOT
fede
devout plinth
so is y^2 = 144
spice snow
right, and now we have to be a bit careful
we can take the square root, but we'll have two solutions
plus or minus
devout plinth
hmmmhm
spice snow
$y = \pm\sqrt{144}$
jolly parrotBOT
fede
jolly parrotBOT
fede
spice snow
now, the positive value was the one we already knew, that is, (0,12)
devout plinth
yes
spice snow
so the other point that is at that distance is...
devout plinth
(0,-12)
spice snow
that's right
devout plinth
yayy
spice snow
and that's it
devout plinth
thank you
i completely forgot all the formulas used in algebra so i was struggling lol
i get it now though
spice snow
np!
devout plinth
.close
pearl pondBOT
pearl pondBOT
Available help channel!
graceful nexus
if f(n) = (n)(logn) and g(n) = (logn) = what is f= ? (g)?
pearl pondBOT
if f(n) = (n)(logn) and g(n) = (logn) = what is f= ? (g)?
graceful nexus
would this be f (Omega) (g)?
pearl pondBOT
@graceful nexus Has your question been resolved?
graceful nexus
.close
silver pasture
I don’t understand why it’s C
pearl pondBOT
I don’t understand why it’s C
solid ivy
I mean just intuitively think about the graphs
one makes a _/
The other makes a /-
you could formalize this with l'hôpitals rule ig
rough stream
Hopefully it's clear, for each of the rows, which function "is larger than" which
C is unique in that the "larger" function is in the denominator
silver pasture
C is unique in that the "larger" function is in the denominator
What about e^x / x^2
rough stream
e^x gets larger than x²
So e^x / x² approaches infinity
,w graph e^x / x^2 between 0.5 and 10
jolly parrotBOT
silver pasture
Is there a chart where I can know which x values grow faster
rough stream
For a while x² can hold e^x off, but e^x really blows up after a while
- Exponentials are always bigger than
- Polynomials, which are always bigger than
- logarithms
That's basically the chart haha
C has a logarithm over an exponential, so that function gets very small, and approaches 0.
silver pasture
Isn't e^x slower than x^2? That would result in denominator growing faster and equaling to 0
jolly parrotBOT
pearl pondBOT
@silver pasture Has your question been resolved?
jagged ridge
can someone help me find the table of values of this quadratic function
h(t)=-16t²+30t+5
fossil lodge
is there some specific values you want to evaluate for?
fossil lodge
h(0) is the initial height in feet right?
Yes. At time = 0, h(t) models the height of the object. So h(0) is the initial height
west sapphire
h(2) is already wrong
misty nymph
no it is not correct
jagged ridge
okay
fossil lodge
can you show how you evaluated h(2)?
fossil lodge
Your function is $h(t) = -16t^2 + 30t + 5$
jolly parrotBOT
WhoTao
fossil lodge
Evaluating h(t) at t = 2, you literally replace wherever you see a t with 2
For example, $-16t^2$, you replace t with a 2. So it becomes $-16(2)^2$
jolly parrotBOT
WhoTao
fossil lodge
your mistake here, is that you did not use that the first term is $-16t^2$. Instead you used $-16t$
jolly parrotBOT
WhoTao
feral leaf
your mistake here, is that you did not use that the first term is $-16t^2$. Inst...
I think she just forgot the ^2 part because if you look at the right, it says -16 * 4 and 4 = 2^2
fossil lodge
Ok. So you should have $h(2) = -16(2)^2 + 30(2) + 5 = -16(4) + 65 = -64 + 65 = -1$
jolly parrotBOT
WhoTao
fossil lodge
So you mustve made a mistake computing -16(4) + 65
jagged ridge
I think she just forgot the ^2 part because if you look at the right, it says -1...
this guy helped me also:)
feral leaf
Ok. So you should have $h(2) = -16(2)^2 + 30(2) + 5 = -16(4) + 65 = -64 + 65 = -...
-64 + 65 = 1
Not -1
jagged ridge
@fossil lodge
feral leaf
<@437300702960812033>
Nope
fossil lodge
what is 3^2?
jagged ridge
h(3)
feral leaf
$3^2 \neq 3 \cdot 2$
jolly parrotBOT
CaptainNova22
fossil lodge
What is the value of 3^2
jagged ridge
I thought its gonna be 3^2 cause im solving for h(3)
jagged ridge
6
jagged ridge
wha
fossil lodge
$3^x$ means you are multiplying $3$ by itself $x$ times.
jolly parrotBOT
WhoTao
jagged ridge
oh so 9
jagged ridge
ohh so -49?
fossil lodge
yes
go to this website
type in
h(t)=-16t^2+30t+5
then type in h(a), where a is the number you want to evaluate function h(x) at
then you can chek your answer
jagged ridge
<@437300702960812033>
ill just solve it using like this
fossil lodge
fossil lodge
you are missing a equal sign
fossil lodge
What type of function is h(x)?
Linear? Quadratic? log? absolute value?
You also have a table of values
just connect the dots on your graph based on your function type
jagged ridge
Quadratic
help
@fossil lodge can u tell me if this is correct? I googled it
am going to school so i gotta do this fastt
pearl pondBOT
@jagged ridge Has your question been resolved?
pearl pondBOT
@jagged ridge Has your question been resolved?
ornate hill
I need help solving geometric sequences and my assignment is already past due 😭
pure sail
ask
ornate hill
what do i need to ask? (Sorry im new here)
okay uh is there a formula for finding geometric series?
looking for the S term
Hello
?
<@&286206848099549185> sorry for ping
pearl pondBOT
<@&286206848099549185> sorry for ping
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
ornate hill
okay uh is there a formula for finding geometric series?
here
unborn abyss
like if you have 1 + 3 + 9 + ... + 3^5 is there a formula for the sum?
unborn abyss
sure
ornate hill
sorry its side ways
unborn abyss
,rccw
jolly parrotBOT
unborn abyss
for an infinite one it's $\f a{1-r}$ where $a$ is the first term and $r$ is the rtio
jolly parrotBOT
haylsGhost
ornate hill
okay
unborn abyss
important: that only works if r is less than 1
ornate hill
ill keep note for that, but what about the other problem like the find S 11
sleek estuary
You can get this by simple Google search
ornate hill
You can get this by simple Google search
I tried but I couldn't find any for the specific one. Unless I'm writing it wrong. sorry if i'm being difficukt
nevermind I found
one last thing
actually nvm
sorry
imma just close
thanks for the help
.close
pearl pondBOT
pearl pondBOT
Available help channel!
carmine root
pearl pondBOT
carmine root
To translate:
Look at the following function g(x) = f(x^2). Show that the following is true: T_4g(x)=T_2f(x^2)
It is around the point a = 0
where f : R -> R where the function satisfies f(^n) exists for all n
How does one start such a problem?
unborn abyss
what are T2 and T4?
pearl pondBOT
@carmine root Has your question been resolved?
carmine root
what are T2 and T4?
sorry i didnt ping the reply
i think this should work as a ping
carmine root
and see if it works?
pearl pondBOT
@carmine root Has your question been resolved?
carmine root
i think if you just write the notional Taylor series for f
my question is though
to show that they are different
do i expand g(x) and f(x^2)?
but it says g(x)=f(x^2)
pearl pondBOT
pearl pondBOT
Available help channel!
limpid jasper
how did they simplify this?
limpid jasper
<@&286206848099549185> 😔😔😔
r u doing ok
y not 😔
@midnight haven bro can u help pls 😭😭😭😭🙏
ur my only hope
ok ok lemme try
omg ok i get it thxxxx
.close
pearl pondBOT
olive dove
what happened in this line?
where did the 1/2 come from
whats A and whats B?
how do i calculate them
alright thank youu
thanksss
pearl pondBOT
@olive dove Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
lone juniper
please. help. me.
pearl pondBOT
please. help. me.
sick adder
lone juniper
can you explain to me
how that simplification happens
because i dont understand
x^3 where does it come from?
😦
sick adder
The first and third rationals have been multiplied by x/x so that the denominators are the same
So it becomes this:
lone juniper
yes
sick adder
$-\frac{x(x^2-2x+1)e^{-x}}{5x^2} - \frac{(x^2-2x+1)^{-x}}{5x^2} + \frac{x(2x-2)e^{-1}}{5x^2}$
jolly parrotBOT
M. Frost
lone juniper
ooooooooooooooooooooooooooooooo
sick adder
Now distribute the x's and then do your addition/subtraction
sick adder
but only the first and third terms, because the second already has 5x^2 as a denominator
lone juniper
sick adder
Essentially before you can add them together you need a common denominator
Try simplifying it from that point on and see what you get
lone juniper
but *only* the first and third terms, because the second already has 5x^2 as a d...
wat
oh yes
thank you
.close
pearl pondBOT
lone juniper
.reopen
pearl pondBOT
✅
sick adder
$\frac{x\left((2x-2)e^{-x} - (x^2 - 2x + 1)e^{-x}\right) - \left(x^2-2x+1\right)e^{-x}}{5x^2} = \frac{x\left((2x-2)e^{-x}\right)}{5x^2} - \frac{x\left(x^2-2x+1\right)e^{-x}}{5x^2} - \frac{\left(x^2-2x+1\right)e^{-x}}{5x^2}$
When those are broken up, you can cancel the x in the nominator with one of the x's in the denominator for those two terms
lone juniper
oooooooooooooooooooooooooooooooooooooooooooooooo
sick adder
Leaving you with 5x in the denominator of two of them, and 5x^2 in the third
jolly parrotBOT
M. Frost
pale iris
I am stuck, my answer appears to be 1/5arcsin(u), I selected this answer only to find out it's wrong. I have a feeling it's because of the constants I moved out front but I'm hoping someone here in the community can show me where my error lies.
pearl pondBOT
I am stuck, my answer appears to be 1/5arcsin(u), I selected this answer only to...
@pale iris Has your question been resolved?
pale iris
Khan Academy doesn't seem to explain exactly how the integral is calculated but I am running through my work and it just seems like 1/5 needs to be there.
pearl pondBOT
@pale iris Has your question been resolved?
pale iris
I am trying very hard to understand what's wrong here but after talking it through with ChatGPT I am more lost because I don't know where I went wrong really, chatGPT isn't gonna get it right either because I have no idea why it's like this. Here is what it told me which cannot be true.
pale iris
.close
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
pearl pondBOT
midnight haven
So my input domain is $\Omega^{25}$ let's denote it as $I$ for input
Where $\Omega = {\emptyset, A, B,..., Z}$
midnight haven
My task is to find the amount of operations I have to perform on I so that the target string denoated as T satisfies the following condition $T \subseteq I_n$ after n operations
jolly parrotBOT
<:F_button:1095679234497843251>
jolly parrotBOT
<:F_button:1095679234497843251>
Should I just do
jolly parrotBOT
<:F_button:1095679234497843251>
midnight haven
where $\Omega = {A,B,...,Z}$
jolly parrotBOT
<:F_button:1095679234497843251>
midnight haven
The task is to count the number of operations required to be performed on I for it to contain a target subset T
Where T is $\Omega^m$
jolly parrotBOT
<:F_button:1095679234497843251>
midnight haven
and an operations is a mapping of I $f: I \rightarrow (I,I)$
jolly parrotBOT
<:F_button:1095679234497843251>
midnight haven
$T \subseteq I_n$ where $I_n$ is the tuple(ordered pair?) $I$ after n operations
jolly parrotBOT
<:F_button:1095679234497843251>
pearl pondBOT
@midnight haven Has your question been resolved?
pearl pondBOT
@midnight haven Has your question been resolved?
Available help channel!
Available help channel!
tiny dagger
pearl pondBOT
tiny dagger
so i had a math test today and i wrote the equation in red
and ig the uniform way to do it is in blue
would i get points off even though they form the exact same graph
blissful cloak
depends on the instructor, technically the generalized absolute value is of the form $a|x-b|+c$, if it was up to me I wouldn't
worst case you can always take it up with your instructor after they grade it :)
tiny dagger
awesome ty!!
jolly parrotBOT
PajamaMamaLlama
tiny dagger
.close
pearl pondBOT
blissful cloak
awesome ty!!
pearl pondBOT
Available help channel!
regal abyss
I wonder when we have the original function of y = f(x)^2, will the transformation be y = f(2(x+3)^2) or y = f(2(x+3))^2? One has the exponent inside, the other has the exponent outside.
regal abyss
And if given y = f(1/2x+3), when I factor 1/2 out to find the transformation, will the function become y = f(1/2(x+6)) or y = f(1/2(x+3))?
pearl pondBOT
@regal abyss Has your question been resolved?
pearl pondBOT
@regal abyss Has your question been resolved?
pearl pondBOT
@regal abyss Has your question been resolved?
regal abyss
<@&286206848099549185>
pearl pondBOT
@regal abyss Has your question been resolved?
pearl pondBOT
@regal abyss Has your question been resolved?
regal abyss
<@&286206848099549185>
pearl pondBOT
@regal abyss Has your question been resolved?
tacit mulch
<@654075381401518096> Has your question been resolved?
I know you've been waiting a long time but
$f\left(\frac{1}{2}x + 3\right) = f\left(\frac{1}{2}(x+ 6)\right)$
jolly parrotBOT
tatpoj
tacit mulch
After all, if you distribute on the right, (1/2) times 6 is 3, right?
pearl pondBOT
@regal abyss Has your question been resolved?
regal abyss
After all, if you distribute on the right, (1/2) times 6 is 3, right?
Yes I understand this
regal abyss
I wonder when we have the original function of y = f(x)^2, will the transformati...
Any ideas on this one?
lament falcon
I wonder when we have the original function of y = f(x)^2, will the transformati...
not rlly the same
bc that for ^2 outside is the result of f(x) ^2
other one have f(x), but it's x who ^2
pearl pondBOT
@regal abyss Has your question been resolved?
vast holly
pearl pondBOT
vast holly
Let V = R^3x3 be the real vector space with all 3 x 3 matrices with real coefficients. There si given following three subparts of V:
- W1, the amount of all triangle matrices in V
- W2, the amount of all diagonalmatrices in V
- W3 = ...
A)
Check that all W1, W2 and W3 are subspaces of V
fluid axle
aight
vast holly
- I do not know what is meant with triangle matrices
- Isn't this obvious?
- Not sure what is meant
fluid axle
this is the idea
fluid axle
for upper triangular matrices, the diagonal and above can be whatever you want
vast holly
with triangle
fluid axle
1. I do not know what is meant with triangle matrices
2. Isn't this obvious?
3....
- if it's obvious to you, you should certainly be able to prove it
vast holly
2. if it's obvious to you, you should certainly be able to prove it
Diagonal is:
100
010
001
Right?
fluid axle
well you can have anything on the diagonal
$\begin{bmatrix} \pi & 0 & 0 \ 0 & \sqrt{2} & 0 \ 0 & 0 & 42\end{bmatrix}$ is diagonal
jolly parrotBOT
aPlatypus
fluid axle
yes
vast holly
number 1: the zero vector in w is in v
number 2: for any u, v in W, u+v is in W
number 3: for any v in W, v*c is in W
so yes, that would make it a subspace
am I right?
fluid axle
those are the conditions for being a subspace yes
vast holly
It should fill those
In a way, W1 and W2 are very similar
So they should both fill those conditions ?
x)
vast holly
well
a scalar for any diagonal still keeps it a diagonal
a diagonal + a diagonal = a diagonal
fluid axle
yeah ok fine I guess
vast holly
a 0 diagonoal is also in V
fluid axle
they're easy to do
vast holly
replace diagonal with triangle and its the same
fluid axle
and now there's no 3
fluid axle
1. I do not know what is meant with triangle matrices
2. Isn't this obvious?
3....
the set of matrices A for which transpose of A = -A
that's what W3 is
fluid axle
it's just a variable to denote which object we're talking about
A belongs to the 3x3 matrices and A = -A^T
and the set is composed all the objects A satisfying these conditions
vast holly
hm
A is a really small group then
well idk
can it even exist
the transposed is where you change row to pillar and pillar to row
how A = - the transposed of A i dont know
jolly parrotBOT
aPlatypus
vast holly
oh i see
fluid axle
you can check it works
they're called antisymmetric matrices
for symmetric matrices you have the equation A^T = A btw
vast holly
well you can also + these together
scalar * asymmetric = assymetric
assymetric + assymetric = assymetric
nvm
001 00-1 000
000 + 000 = 000
-100 100 000
i guess this one is both symmetric and assymetric
001 00-5 00-4
000 + 000 = 000
-100 100 000
i guessn this is a better example of why it doesnt work? @fluid axle
vast holly
wdym
fluid axle
you're adding 3D vectors, or I'm misunderstanding completely what you wrote
vast holly
im adding 3x3 matrices
vast holly
?
vast holly
oh true
cuz the number is not the same in both places
is:
000
000
000
considered assymetric? @fluid axle
fluid axle
yes
0 matrix transposed is also the 0 matrix, and 0 = -0
you have to work with the A = -A^T condition
fluid axle
well it is
vast holly
well it is
next i need to find the basis and dimensions
fluid axle
you haven't really justified why
gonna need more than, oh diagonal + diagonal = diagonal this time
vast holly
well first of all the 0 vector is in both
asymmetric + asymmetric kan result in a normal asymmetric or just the 0 vector
but the 0 vector is also regarded as asymmetric
is there more to it than that?
oh and if you take the scalar of the asymmetric you also get an asymmetric one
fluid axle
asymmetric + asymmetric kan result in a normal asymmetric or just the 0 vector
this is too vague
that's my issue
vast holly
Maybe im not good at explaining
fluid axle
you know antisymmetric matrices satisfy A = -A^T
so say I take two matrices A and B, with A = -A^T, and B = -B^T
and you want to show C = A+B satisfies C = -C^T
fluid axle
if you manage to show that, you show that the sum of two matrices in W3 is also in W3
vast holly
you mean V?
fluid axle
it's what your question called it
vast holly
$\begin{bmatrix} 0 & 0 & -1 \ 0 & 0 & 0 \ 1 & 0 & 0\end{bmatrix}$
jolly parrotBOT
ehd
vast holly
wtf
fluid axle
you need to add the double slashes back between the lines
vast holly
$\begin{bmatrix} 0 & 0 & 1 \ 0 & 0 & 0 \ -1 & 0 & 0\end{bmatrix}$
jolly parrotBOT
ehd
fluid axle
yes
vast holly
00-x 00-y 00-x-y
000 + 000 = 000
x00 y00 x+y00
regardless of value of x and y, you end up with a product that is assymmetric
fluid axle
yes
my point is that you don't need to find all the antisymmetric matrices explicitly
just work with the condition given to be an antisymmetric matrix
fluid axle
C^T you mean
fluid axle
wait nvm my brain fried for a second
fluid axle
C = -A^T -B^T
that is true indeed
vast holly
yeah
fluid axle
you want to make appear (A+B)^T = C^T in your equality somehow
fluid axle
I'm saying the thing you have to show has C^T in it
fluid axle
yeah exactly that works
C = A + B
= -A^T - B^T
therefore
-C = A^T+B^T
= (A+B)^T
= C^T
so C = -C^T
so if A and B are antisymmetric, then C=A+B is also antisymmetric
fluid axle
it's certainly easier than trying to find what all the antisymmetric matrices look like
fluid axle
it's certainly easier than trying to find what all the antisymmetric matrices lo...
but you'll have to do this anyway if you want a basis
vast holly
it's certainly easier than trying to find what all the antisymmetric matrices lo...
x)
true
Why is this listed as a possible basis when you cannot create:
100
000
00-1
@fluid axle
vast holly
oh
I dont get it though
why is this the base
when thsi si the basis for W2
Would 1 0 0
0 0 0
0 0 0
also be considered a diagonal matrix ?
fluid axle
if you think more about A^T = -A, it means that the elements swapped around the diagonal are opposites of one another
fluid axle
Would 1 0 0
0 0 0
0 0 0
also be considered a diagon...
yes
vast holly
So the basis is a representation of all possible combinations with a scalar
fluid axle
vast holly
but the basis in w2 doesnt give us something that results in:
100
010
001
fluid axle
but the basis in w2 doesnt give us something that results in:
100
010
001
so what ?
you can also get
100
000
000
with this basis
vast holly
so theres an infinite amount of basis?
2 0 0
0 0 0
0 0 0
you can also get
100
000
000
with this
fluid axle
you can write all diagonal matrices as a linear combination of
100
000
000
000
010
000
000
000
001
there are infinitely many diagonal matrices
vast holly
okay, I get it
fluid axle
but you can get them all from those three matrices in the basis
vast holly
right, and you can get all assymetric with a linear combination of:
fluid axle
yes
vast holly
and we are allowed to * and + to create new linear combinations right ?
fluid axle
yes
that's what a linear combination is all about
$$\begin{bmatrix}a&0&0 \0 & b &0 \0&0&c\end{bmatrix} = a\begin{bmatrix}1&0&0 \0 & 0 &0 \0&0&0\end{bmatrix} + b\begin{bmatrix}0&0&0 \0 & 1&0 \0&0&0\end{bmatrix} + c\begin{bmatrix}0&0&0 \0 & 0&0 \0&0&1\end{bmatrix} $$
jolly parrotBOT
aPlatypus
fluid axle
you can get all diagonal matrices as a linear combination of the 3 matrices
and there's only one way to do so for each diagonal matrix
that's what makes this set of 3 matrices a basis (of the space of diagonal matrices)
@vast holly
vast holly
right
thanks for dealing with me. I have a lot of questions
You up for some more questions?
fluid axle
yup
nimble osprey
vast holly
indeed
Which of the following are subspaces of C[Z], where C[Z] is a polynomial with complex coefficients
fluid axle
okey
vast holly
Well the first one is basically a copy of C[Z] right?
the 0 polynomial is also just 0 in C[Z]
fluid axle
yup, this one's not too hard
now there's still the sum and the multiplication to look at
fluid axle
(you prolly don't want to write all the polynomials with p(0) = 0)
fluid axle
its a copy
wdym specifically ?
vast holly
i dont know how to explain it better
fluid axle
its a copy
there's a way to argue like that rigorously (with isomorphisms), but it's convoluted and not the point of an intro question like that
it's mostly to see if you know well the definition of what a subspace is, and you are able to use it effectively on examples
vast holly
How would you word it?
fluid axle
there's also the problem that if you haven't seen what isomorphisms are, it's just gonna be completely arcane to you
but the basic idea is, look at the map $F : \mathbb C [Z] \to W_1$, defined by $$F( p(Z) ) = Zp(Z)$$
jolly parrotBOT
aPlatypus
fluid axle
it's a linear map, and it's bijective (for each output in W1, you have a unique input polynomial in C[Z] which corresponds to it)
so that essentially means that W1 is a copy of C[Z]
but the problem is that for the concept of linear map to make sense, you need to know that W1 is a vector space already
so that argument justfies the copy part, you still need to know that W1 is a subspace
you won't avoid using the definition of subspace
it will drilled in your brain forever
@vast holly
vast holly
there's also the problem that if you haven't seen what isomorphisms are, it's ju...
I dont kno wisomorphisms
vast holly
you won't avoid using the definition of subspace
haha
yeah
but I think I got a clear idea now
a subspace is a vector space where all combinations are true for another space with a higher number of combinations
fluid axle
and those combinations stay in the subspace, they don't end up in the bigger space
vast holly
and ofc where all combinations are a result of addition and multiplication
and yes stay within the defined subspace
fluid axle
yep indeed
fluid axle
number 1: the zero vector in w is in v
number 2: for any u, v in W, u+v is in W
...
^
that's essentially what the conditions 2 and 3 mean
fluid axle
you can't multiply two polynomials together
you can just add polynomials
or scale them by a number
that's the only things you can do in a vector space
the even bigger problem to me is
"what do you do of the zero polynomial?"
vast holly
okay
fluid axle
how do you even talk about the multipliclity of its roots?
fluid axle
Z^2 has 0 as a root of multiplicity 2 already
vast holly
right
oh
yeah so it cant be in
Why did the teacher write that its not a subspace because Z*(Z-1)+Z = Z^2....
I thought we are not allowed to say Z* something since its not a normal scalar??
fluid axle
yeah sorry I guess I screwed up a bit in my terminology (or i was a bit imprecise at least)
Z(Z-1) is a polynomial in its own right
Z^2 - Z if you want
it's just that I had the give a coefficient to each degree vision
vast holly
Z(Z-1)+1*Z = Z^2
fluid axle
you can't say Z is in W1, so Z*Z should be in W2 if W2 should be a subspace though
that's what I was trying to say before
vast holly
your space ?
fluid axle
you can't say Z is in W1, so Z*Z should be in W2 if W2 should be a subspace thou...
changed my sentence
@vast holly
fluid axle
but why isn't Z in W1?
it is
vast holly
haha
fluid axle
and it's getting a bit late anyway
pearl pondBOT
@vast holly Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
dull plover
Is this the same as saying a x^2 + y^2 = 1 circle? (but obv with x_1 & x_2)?
dull plover
not the circle
what do you mean?
dull plover
yeah that is kinda what i meant, should've probably made that distinction. But it would be the same as x^2 + y^2 <= 1?
pearl pondBOT
@dull plover Has your question been resolved?
real scarab
yeah that is kinda what i meant, should've probably made that distinction. But i...
yes
if you are talking about real and imaginary parts
as x and y
dull plover
if you are talking about real and imaginary parts
is it not just on the real plane?
real scarab
this is a complex notation
dull plover
this is the whole context of the question
real scarab
yeah that is kinda what i meant, should've probably made that distinction. But i...
so yeah this is exactly the same as that
midnight haven
.
jolly parrotBOT
<enumitem>
Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health If a member of this senior class is selected at random, find the probability that the student:
\env{enumerate}[[(a)]]{
\ii smokes but doesn't drink alcoholic beverages,
\ii eats between meals and drinks alcoholic beverages but doesn't smoke.
\ii neither smokes nor eats between meals
}
So, we have the following:
\env{alignat*}[{3}]{
\abs A &= 210 &\qq \abs B &= 258 &\qq \abs C &= 216 \\
\abs{A \cap B} &= 122 & \abs{B\cap C} &= 83 &\abs{A\cap C} &= 97 \\
&& \abs{A\cap B \cap C} &= 52 &&
}
So, for (b) the expression for the cardinallity would be $\abs{\overline A \cap B \cap C}$, but I can't seem to find a nice expression to evaluate that from what i have
real scarab
same, BnC =AnBnC + BnCnA'
its like total probabilities theorem its the same
your partition E in A and A'
midnight haven
GOSH
WHY DID I NOT SEE THAT
FSDNF
😭
okay so for (c)
would it be
[
\abs{\overline A \cap \overline C} = \abs B - \abs{A\cap B} -\abs{B\cap C} + \abs{A\cap B \cap C}
]
jolly parrotBOT
real scarab
idk about what the B does
f latex
|A'nC'| = |E| - (|AuC|) = |E| - (|A|+|C| -|AnC|)
midnight haven
what is E
midnight haven
like this is the region right
what A'nC' represents
so its |B| - the intesections with C and A + the intersection of all of them so we dont undercount
oh wait
i see my mistake
okay
real scarab
not A'nC' is just everything thats not AuC
draw C'
and A'
in different colors
like hash it
midnight haven
like this is the region right
it basically becomes the region in red plus the whole rectangle excluding A and C
righht
oksu
okay
i got the idea
thanks a lot!
wait
something is weird
i get 196/500
but the answer key is saying 171/500
ooo nvm
ty
,close
.close
pearl pondBOT
pearl pondBOT
Available help channel!
shy ledge
Is the correct answer to this question: zero for both cases, because the magnitude of the component in which directs to B is the dot product between them, and the dot product between two perpendicular vectors produces zero
shy ledge
^ and vice versa, hence zero for both cases
unborn abyss
yeah
you can also just like think about it: if you're going 100% north then you're going 0% east and west
tulip leaf
Hay everyone.
im stuck on question (f)
I answered this question already and I got -28
But I was wrong as the answer is 44.
.
I got -28 because I calculated 4x first = 8
Then I calculated 6xy = 36.
8 - 36 = -28
calm wing
Hay everyone.
im stuck on question (f)
I answered this question already and I...
you sure 6xy = 36? (hint: if you are, you shouldn't be)
tulip leaf
hi artemetra hope you are well
ill try calculate it again
wait it should be -6xy actually i believe
as there is a - before it
calm wing
uh
vast depot
-(-36)
calm wing
yeah
vast depot
8-(-36)=8+36
tulip leaf
hmm okay so its -6 x 2 x -3 = 36
oh wait you said it wasnt 36 for 6xy
would the correct calculation for 6xy be (-6 x 2 x -3)?
pearl pondBOT
@tulip leaf Has your question been resolved?
tulip leaf
<@&286206848099549185>
glacial wagon
would the correct calculation for 6xy be (-6 x 2 x -3)?
yes you got it
tulip leaf
but it should be -6xy because there is a negative here?
glacial wagon
you’re very welcome!
plain lark
silent pulsar
Hay everyone.
im stuck on question (f)
I answered this question already and I...
first, 6xy=-36
then 4x is 8
tulip leaf
hay croustibest yeah but shouldnt it be -6xy though?
that was what i was confused about
silent pulsar
8-- 36=8+36=44
tulip leaf
because there is a negative sign before 6xy
silent pulsar
yeah cuz 2--2=2+2
u substracted where u should have add
that's all
as -2*-2 =4 and not -4
tulip leaf
oh yeah lol thank you Croustibest
my original calculation for -6xy was -6 x 2 x -3 = 36
tulip leaf
ah yes
I did 8 - 36 which is why my answer was -28 at first.
because it was 4v - 6xy so I thought I had to do 8 - 36.
tulip leaf
appreciate you Croustibest
Have a great night Croustibest
pearl pondBOT
@tulip leaf Has your question been resolved?
sullen lion
pearl pondBOT
worldly glacier