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help-10
ac95ffbf60ed4a87b76d1ef1cd11af86
642,870,756,409,212,900
GymBroYes
04/14/2022 13:45:35
Ok I’ll write it
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ac95ffbf60ed4a87b76d1ef1cd11af86
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GymBroYes
04/14/2022 13:45:47
Took out a factor of 3/2 for the intergral of x
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help-10
ac95ffbf60ed4a87b76d1ef1cd11af86
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GymBroYes
04/14/2022 13:46:01
Then took out a factor of -2 for the integral of 1/x3
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help-10
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lily212
04/14/2022 15:34:17
if you need to make up a basis for a subspace that you have the equation of, I thought you needed to have the same number of vectors in the set as the dimension of the subspace. In one of our Gram-Schmidt process examples, the subspace is x-y+z = 0 but the basis the prof came up with only had two vectors (1,0,-1) and (...
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help-10
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Zorn's Lemon
04/14/2022 15:36:09
If your system is x-y+z=0, you have 2 free variables and 1 dependent variable, so you have a 2-dimensional subspace of R^2
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help-10
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lily212
04/14/2022 15:36:58
oh ok. How do you know that? I saw the x, y, z and assumed it was R^3
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help-10
71387abcab8a43bfab68658da38991ea
484,702,191,156,985,860
themateo713
04/14/2022 15:37:00
The number of variables involved isn't the dimension of the subspace. The number of equations (that are not redundant) determines the number of dimensions you lose. Here since you have 1 equation in 3D you have a 2D vector space. The number of variables used in the equation(s) is irrelevant: x+y+z=0 and x=0 both determ...
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help-10
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lily212
04/14/2022 15:38:02
Oh ok that makes a bit more sense. Could you provide an example of when it would be in R^3?
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:38:05
Vectors in your space look like $\begin{pmatrix}y-z\\y\\z\end{pmatrix}$
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help-10
71387abcab8a43bfab68658da38991ea
510,789,298,321,096,700
TeXit
04/14/2022 15:38:08
**Zorn's Lemon**
https://cdn.discordapp.c…635287855104.png
326954635287855104.png
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:40:00
What you have is the equation defining a specific plane in 3-dimensional space, basically. Try plotting your equation in geogebra 3d to see what you get: https://www.geogebra.org/3d
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help-10
71387abcab8a43bfab68658da38991ea
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lily212
04/14/2022 15:40:10
which one is the dependent variable?
1
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:40:36
The way that I wrote it is with y and z free and x dependent, but you can take your choice of the three
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help-10
71387abcab8a43bfab68658da38991ea
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Zorn's Lemon
04/14/2022 15:41:09
Which is to say, if you know two of your three coordinates, you can use the equation you have to find the third.
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help-10
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lily212
04/14/2022 15:41:22
could you give me an example of when it would be in R^3? Would it need to be two equations?
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:41:36
oh ok
1
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:41:49
that kinda makes sense lol
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:42:02
Well your plane is already in R^3, it's just only part of R^3
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:42:12
Imagine you have a plane with a line on it
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1
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:42:20
The plane is 2d, the line is a 1d subspace of the plane
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:42:29
Defined by 1 equation
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:42:37
This is just the same situation 1 dimension up
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help-10
71387abcab8a43bfab68658da38991ea
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lily212
04/14/2022 15:43:32
I'm still confused on how to tell what the dimension is. If it's in R^3 why doesn't the basis have 3 vectors?
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:44:02
Because it's not all of R^3. The basis has 2 vectors because it's a 2-dimensional part of R^3
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:44:06
Do you have a piece of paper?
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help-10
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lily212
04/14/2022 15:44:13
yeah I do
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:44:19
The piece of paper is 2d, right?
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:44:25
yes
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:44:33
It's in 3d space, right?
0
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:44:39
yes
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:44:54
You can define any point on the piece of paper in 2 vectors
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:45:11
If you have a third vector, it's either not linearly independent so useless, or it points to somewhere not on the piece of paper
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:46:10
oooh that makes sense now.
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:46:12
The subspace you have, a subspace of R^3 defined by your 1 equation, is a 2-dimensional space in R^3. Just like how your piece of paper is a 2-dimensional space in our 3-dimensional world
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:46:57
that does make sense now! Ok One more question would be, what would the equation need to look like if it wasn't a plane but a 3D object?
1
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Zorn's Lemon
5426
Zorn's Blue Raspberry
false
1,875
help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:47:17
Well, we'd be working somewhere other than R^3
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lily212
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lily212
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:47:52
If you wanted a 3d subspace of $\mathbb{R}^4$, you could try a single equation again, and you'd get vectors like $\begin{pmatrix}y-z\\y\\z\\w\end{pmatrix}$.
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help-10
71387abcab8a43bfab68658da38991ea
510,789,298,321,096,700
TeXit
04/14/2022 15:48:13
**Zorn's Lemon**
https://cdn.discordapp.c…635287855104.png
326954635287855104.png
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1
484,702,191,156,985,860
themateo713
5303
mateo713
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:48:25
If you wanted a 3d subspace of $\mathbb{R}^{5}$, it would be defined by two equations. Etc.
0
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Zorn's Lemon
5426
Zorn's Blue Raspberry
false
1,875
help-10
71387abcab8a43bfab68658da38991ea
510,789,298,321,096,700
TeXit
04/14/2022 15:48:28
**Zorn's Lemon**
https://cdn.discordapp.c…635287855104.png
326954635287855104.png
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:49:13
The only 3d subspace of R^3 is R^3 itself. There are shapes in 3d that are proper subsets of R^3 (say, a filled-in sphere), but they aren't vector spaces.
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lily212
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help-10
71387abcab8a43bfab68658da38991ea
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lily212
04/14/2022 15:49:59
oh ok I think that's where I was confused maybe. Because the plane isn't in R^3 but it's just a subspace of R^3
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:50:05
right?
1
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:50:27
Well it's "in" R^3 in the same way as your piece of paper is in our 3-dimensional world
0
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:50:42
Subspaces are indeed proper subsets
0
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:50:50
right but the basis for it is in R^2?
1
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:51:19
The basis for it is vectors in R^3. It happens to be that it is isomorphic to R^2 as a vector space, but it is not itself R^2
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:51:49
Oh ok
1
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:52:02
I think I understand it a lot better now
1
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:52:24
Put in some practice and I'm sure you'll get it.
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:52:50
thank you so much!
1
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help-10
71387abcab8a43bfab68658da38991ea
326,954,635,287,855,100
Zorn's Lemon
04/14/2022 15:53:19
If you're done remember to .close
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help-10
71387abcab8a43bfab68658da38991ea
695,354,943,384,715,400
lily212
04/14/2022 15:53:59
.close
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456,226,577,798,135,800
Deleted User
04/14/2022 16:33:37
https://cdn.discordapp.c…t_3.33.33_PM.png
Screen_Shot_2022-04-14_at_3.33.33_PM.png
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Deleted User
04/14/2022 16:34:14
aa
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help-10
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live
04/14/2022 17:34:36
hello ive came across problem that im a bit confused with: basically u need to express point B with a, ive tried to play around with coefficients because both lines are tangents of parabola, however then idk what to do
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live
04/14/2022 17:34:39
https://cdn.discordapp.c…unknown-5-12.png
unknown-5-12.png
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help-10
0b4f2bbeaf6543cfa6f6938adeabf6a0
282,640,167,733,559,300
live
04/14/2022 17:34:45
https://cdn.discordapp.c…20415_002102.jpg
IMG_20220415_002102.jpg
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help-10
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live
04/14/2022 17:34:48
heres my thought process
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:53:37
.reopen
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:54:59
i think yes, but consider it as a application math question
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help-10
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yes sam
11/12/2021 21:56:00
See
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:56:12
Isolated terms with S
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:56:28
Like x=y
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:56:44
3x=2y+2z
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:56:58
what it means, isolate the S?
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PB
11/12/2021 21:57:05
ohh
1
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yes sam
11/12/2021 21:57:42
I mean don't think about O just observe xS -> yS
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help-10
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PB
11/12/2021 21:57:59
X(S+3O)=Y(S+2O)+Z(2O)
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:58:07
Yes
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:58:33
then what should i do next it looks terrible
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:58:58
Look at thia
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2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:59:33
i can't follow
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 21:59:40
Treat S and O as different variables
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 21:59:48
ok
1
0
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help-10
2c1c0e6dd9424028873ac4024a806585
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PB
11/12/2021 22:01:15
should i do expanding them
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0
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help-10
2c1c0e6dd9424028873ac4024a806585
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yes sam
11/12/2021 22:01:29
Do you know number of S on right should be equal to number of S in left
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null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:01:40
yes
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:01:43
So u don't have to do this much
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:02:00
so x must be equals to y
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:02:02
am i right
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:02:18
On left there are x S and on right there are y S So x=y
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:02:39
ohhh
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:02:51
let me write it down
1
0
734,794,827,077,648,600
yes sam
5028
fäf
false
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:05:11
x=2, y=2, z=1
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:05:13
am i right
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:05:42
I wont give answer
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:05:57
https://cdn.discordapp.c…540/IMG_6549.jpg
IMG_6549.jpg
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:06:31
6O=4O+2O
1
0
734,794,827,077,648,600
yes sam
5028
fäf
false
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:06:53
:thinkies:
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:06:59
x=y=2,z=1
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:07:04
and that's it
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:07:44
is there anything wrong
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:08:06
maybe its the way i approaching to it?
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:08:25
Wait
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:09:05
I don't get whachu did
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:09:27
make a table of x=y and z
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:09:32
then put the numbers in
1
0
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
734,794,827,077,648,600
yes sam
11/12/2021 22:09:46
Wait I'll just write it
0
1
null
null
null
null
null
1,879
help-10
2c1c0e6dd9424028873ac4024a806585
708,594,064,060,055,600
PB
11/12/2021 22:09:51
ok
1
0
null
null
null
null
null