#matrix help

72 messages · Page 1 of 1 (latest)

peak sail
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So I have to find the matrix of this picture I don’t really know how to do this can’t really find how to do it

IMG_0904.png
iron kilnBOT
peak sail
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I would love just a point in the right direction

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Oh and the problem asks to find the matrix of the left graph and use linear mapping to get the right side if that makes sense

unique rain
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what you can do is look at how some specific points of the figure changed from left to right

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for example, what happens to the bottom left of the K when you go from the 1st picture to the 2nd ?

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@peak sail

peak sail
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Goes from a straight line where x=0 to one that goes from x=0 to x=2

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But i dont get how to find the matrix of that

unique rain
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no, the bottom left stays put, it doesn't move

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(0,2) in the first pic is (0,2) in the second pic also

peak sail
unique rain
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now yeah we can talk about the top left of the K if you want

peak sail
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Point moves from 0,6 to 2,6

unique rain
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yep

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so let's say our transformation matrix from 1st pic to 2nd pic is called T

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what can you say about T from these two pieces of info ?

peak sail
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I’m not really sure how you make this matrix but the points on the bottom (y=0) is the same in both of the matrix but they shift by +2 at y=6

unique rain
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my goal is to get the matrix from knowing how these 2 points move

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indeed we don't know what T is yet

peak sail
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So wait is t how we change left side to make ther right side

unique rain
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yeah

peak sail
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So like LT=R L=left side R=right side?

unique rain
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yeah T*L = R

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where L is a point on the left side

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and R is the corresponding point on the right

peak sail
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Ahhhh ok

unique rain
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so if you plug in these two pairs of L/R points we got earlier

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what equations do we get ?

peak sail
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T x [0 6] = [2 6]

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Am i doing that right ?

unique rain
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yeah assuming you mean column vectors for your points (it's hard to type them on text ik)

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T goes from R^2 to R^2, so it's gonna be a 2x2 matrix

peak sail
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So in the 2x2 matrix Will it be the highest and lowest point

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So 2,6 and 0,6 in the 2x2 matrix

unique rain
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not sure what you're saying here

peak sail
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Wait nvm i missread

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Ok so T is a 2x2 matrix

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Wich makes the matrix with [0 6] into a matrix [2 6]

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And just so im doing this correct R and L are 1x2 and not 2x1

unique rain
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2x1 they should be

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otherwise the matrix-vector product doesn't make sense

peak sail
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Yeah my bad i meant the other way around 2x1 not 1x2

unique rain
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$$T\begin{bmatrix}0 \ 6\end{bmatrix} = \begin{bmatrix}2 \ 6\end{bmatrix}$$
$$T\begin{bmatrix}2 \ 0\end{bmatrix} = \begin{bmatrix}2 \ 0\end{bmatrix}$$

tranquil thicketBOT
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aPlatypus

177516015033384960.png
unique rain
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so that's what we got

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2 equations about T

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now it turns out we can combine these 2 equations into 1

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by the power of matrices again

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$$T\begin{bmatrix}0 & 2 \ 6 & 0\end{bmatrix} = \begin{bmatrix}2 & 2 \ 6 & 0\end{bmatrix}$$

tranquil thicketBOT
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aPlatypus

177516015033384960.png
unique rain
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I matched the columns together

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[L_1 | L_2] gives [R_1 | R_2]

peak sail
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Yes that makes sense

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Do we do this for every important point?

unique rain
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2 are sufficient

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we're working in R^2 that's why

peak sail
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Alright ill do the calculation

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See if i get this 1 second

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1,1 is 1/3

IMG_0905.jpg
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Does this look correct

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This should be T

unique rain
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,w {{2, 2}, {6,0}} * {{0,2}, {6,0}}^-1

tranquil thicketBOT
unique rain
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well maybe you swapped the columns at some point

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but it looks roughly good

peak sail
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Yes ok i see Where i went wrong i didnt put it back into the correct spots

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I get the same answer as you sent now

unique rain
peak sail
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Thank you for the help!! ❤️

unique rain
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you can use .close if you're done @peak sail

peak sail
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.close