Question

I need someone that's good at matrices!! PLEASE HELP :'(

Answer 1

@amistre64

Answer 2

I've been doing math all day and this is my last problem and I've never seen one like it before please help!!

Answer 3

@iambatman @jigglypuff314 @Preetha

Answer 4

Can you post the "illustrated motion?"

Answer 5

oooh! I didn't even see it yes I will @mathmate

Answer 6

So this is a clockwise rotation about the origin, right?

Answer 7

Sorry, counter-clockwise rotation about the centre of 90 degrees per frame.

Answer 8

counter-clocwise right?

Answer 9

right

Answer 10

There is a matrix for r90. Do you know it by heart, or do you use the general matrix to rotate angle \(\theta\)?

Answer 11

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

Answer 12

Have you done translation matrices?

Answer 13

no... the furthest I've gone is inverted matrices...

Answer 14

So you know how to multiply a matrix?

Answer 15

yes

Answer 16

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.

Answer 17

ok

Answer 18

R=
cos(theta) -sin(theta)
sin(theta) cos(theta)

Answer 19

oh ok

Answer 20

so with this problem...?

Answer 21

and the points matrix would be
x1 x2 x3 x4... xn
y1 y2 y3 y4 ... yn

Answer 22

alright

Answer 23

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.

Answer 24

Each multiplication will rotate Pn by 90 degrees, CCW.

Answer 25

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.

Answer 26

ok I'm a bit lost... how would I write the matrices?

Answer 27

They were both given earlier, R, and Pn.
The multiplication is only RRRRP

Answer 28

oooh! alright I see. so how would the finished problem look?

Answer 29

Do you find the matrices? I did not format them.

Answer 30

yes I see, where you said the points matrix, and R

Answer 31

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?

Answer 32

(sorry for the sloppy formatting)

Answer 33

ok... the formatting is a little hard to follow but I think I get it...

Answer 34

so is that the answer to my problem?

Answer 35

@mathmate ?

Answer 36

Not yet, you need to create Pn to represent the 4 points, then you can do the rotations.

Answer 37

can you show me? @mathmate

Answer 38

better formatting like this?

Answer 39

you have been soooo extremely helpful I wish i could thank you more!

Answer 40

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!

Answer 41

can you show me what the matrix would look like?

Answer 42

I'm sorry I'm not very smart :(

Answer 43

Dont understimate yourself! :)

Answer 44

oh boy... I'm lost :( can you show me the next one so I can see the changes?

Answer 45

0 -2 ...
-1 -3...
for all 4 points

Answer 46

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?

Answer 47

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.

Answer 48

I'm just going to leave it like that and get half credit, thank you for your help.

Answer 49

Sorry! :(