anonymous
  • anonymous
I need someone that's good at matrices!! PLEASE HELP :'(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
@amistre64
anonymous
  • anonymous
I've been doing math all day and this is my last problem and I've never seen one like it before please help!!

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More answers

anonymous
  • anonymous
@iambatman @jigglypuff314 @Preetha
mathmate
  • mathmate
Can you post the "illustrated motion?"
anonymous
  • anonymous
oooh! I didn't even see it yes I will @mathmate
anonymous
  • anonymous
1 Attachment
mathmate
  • mathmate
So this is a clockwise rotation about the origin, right?
mathmate
  • mathmate
Sorry, counter-clockwise rotation about the centre of 90 degrees per frame.
anonymous
  • anonymous
counter-clocwise right?
anonymous
  • anonymous
right
mathmate
  • mathmate
There is a matrix for r90. Do you know it by heart, or do you use the general matrix to rotate angle \(\theta\)?
anonymous
  • anonymous
I've never done rotated matrices before! I never learned it I don't know why they gave me this problem... please just show me step by step how you would do it
mathmate
  • mathmate
Have you done translation matrices?
anonymous
  • anonymous
no... the furthest I've gone is inverted matrices...
mathmate
  • mathmate
So you know how to multiply a matrix?
anonymous
  • anonymous
yes
mathmate
  • mathmate
A rotation matrix R (in 2d) is a 2x2 matrix, when premultiplied to a 2x n matrix will rotate the n sets of coordinates by an angle theta.
anonymous
  • anonymous
ok
mathmate
  • mathmate
R= cos(theta) -sin(theta) sin(theta) cos(theta)
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
so with this problem...?
mathmate
  • mathmate
and the points matrix would be x1 x2 x3 x4... xn y1 y2 y3 y4 ... yn
anonymous
  • anonymous
alright
mathmate
  • mathmate
We'll call the points matrix Pn (for n points). So create the R matrix for +90 degrees, and the P matrix for the pattern required.
mathmate
  • mathmate
Each multiplication will rotate Pn by 90 degrees, CCW.
mathmate
  • mathmate
For eight frames, you will multiply eight times. so RRRRPnPnPnPn with bring you back to the original position. Do that again will give you 8 frames.
anonymous
  • anonymous
ok I'm a bit lost... how would I write the matrices?
mathmate
  • mathmate
They were both given earlier, R, and Pn. The multiplication is only RRRRP
anonymous
  • anonymous
oooh! alright I see. so how would the finished problem look?
mathmate
  • mathmate
Do you find the matrices? I did not format them.
anonymous
  • anonymous
yes I see, where you said the points matrix, and R
mathmate
  • mathmate
So to rotate 90 degrees, it's RP,. Say \(P=(2,1)^T\) and R 90 = 0 -1 1 0 by subst. cos(90) and sin(90). So multiply 0 -1 1 0 by 2 1 you'll get -1 2 get the idea?
mathmate
  • mathmate
(sorry for the sloppy formatting)
anonymous
  • anonymous
ok... the formatting is a little hard to follow but I think I get it...
anonymous
  • anonymous
so is that the answer to my problem?
anonymous
  • anonymous
@mathmate ?
mathmate
  • mathmate
Not yet, you need to create Pn to represent the 4 points, then you can do the rotations.
anonymous
  • anonymous
can you show me? @mathmate
anonymous
  • anonymous
better formatting like this?
1 Attachment
anonymous
  • anonymous
you have been soooo extremely helpful I wish i could thank you more!
mathmate
  • mathmate
The shape is made up of 4 points at frame 1. You make a 2x4 matrix to represent the 4 points, then premultiply by R, you'd get frame 2. But check the results!
anonymous
  • anonymous
can you show me what the matrix would look like?
anonymous
  • anonymous
I'm sorry I'm not very smart :(
mathmate
  • mathmate
|dw:1433211807693:dw| Dont understimate yourself! :)
anonymous
  • anonymous
oh boy... I'm lost :( can you show me the next one so I can see the changes?
mathmate
  • mathmate
0 -2 ... -1 -3... for all 4 points
anonymous
  • anonymous
I'm so sorry to ask this... and you can of course say no, but I'm supposed to show my work, its late, I've been doing math literally all day... could you please show me what the answer / end result would look like so I can be done?
mathmate
  • mathmate
I am sorry I cannot do that. But I think you are able to solve the problem if you can identify the vertices of the shape, and do matrix multiplication. I can help you check when you finish, or attempted.
anonymous
  • anonymous
I'm just going to leave it like that and get half credit, thank you for your help.
mathmate
  • mathmate
Sorry! :(

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