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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @amistre64

  3. anonymous
    • one year ago
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    I've been doing math all day and this is my last problem and I've never seen one like it before please help!!

  4. anonymous
    • one year ago
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    @iambatman @jigglypuff314 @Preetha

  5. mathmate
    • one year ago
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    Can you post the "illustrated motion?"

  6. anonymous
    • one year ago
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    oooh! I didn't even see it yes I will @mathmate

  7. anonymous
    • one year ago
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  8. mathmate
    • one year ago
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    So this is a clockwise rotation about the origin, right?

  9. mathmate
    • one year ago
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    Sorry, counter-clockwise rotation about the centre of 90 degrees per frame.

  10. anonymous
    • one year ago
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    counter-clocwise right?

  11. anonymous
    • one year ago
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    right

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

  13. anonymous
    • one year ago
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    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

  14. mathmate
    • one year ago
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    Have you done translation matrices?

  15. anonymous
    • one year ago
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    no... the furthest I've gone is inverted matrices...

  16. mathmate
    • one year ago
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    So you know how to multiply a matrix?

  17. anonymous
    • one year ago
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    yes

  18. mathmate
    • one year ago
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    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.

  19. anonymous
    • one year ago
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    ok

  20. mathmate
    • one year ago
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    R= cos(theta) -sin(theta) sin(theta) cos(theta)

  21. anonymous
    • one year ago
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    oh ok

  22. anonymous
    • one year ago
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    so with this problem...?

  23. mathmate
    • one year ago
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    and the points matrix would be x1 x2 x3 x4... xn y1 y2 y3 y4 ... yn

  24. anonymous
    • one year ago
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    alright

  25. mathmate
    • one year ago
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    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.

  26. mathmate
    • one year ago
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    Each multiplication will rotate Pn by 90 degrees, CCW.

  27. mathmate
    • one year ago
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    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.

  28. anonymous
    • one year ago
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    ok I'm a bit lost... how would I write the matrices?

  29. mathmate
    • one year ago
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    They were both given earlier, R, and Pn. The multiplication is only RRRRP

  30. anonymous
    • one year ago
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    oooh! alright I see. so how would the finished problem look?

  31. mathmate
    • one year ago
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    Do you find the matrices? I did not format them.

  32. anonymous
    • one year ago
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    yes I see, where you said the points matrix, and R

  33. mathmate
    • one year ago
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    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?

  34. mathmate
    • one year ago
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    (sorry for the sloppy formatting)

  35. anonymous
    • one year ago
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    ok... the formatting is a little hard to follow but I think I get it...

  36. anonymous
    • one year ago
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    so is that the answer to my problem?

  37. anonymous
    • one year ago
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    @mathmate ?

  38. mathmate
    • one year ago
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    Not yet, you need to create Pn to represent the 4 points, then you can do the rotations.

  39. anonymous
    • one year ago
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    can you show me? @mathmate

  40. anonymous
    • one year ago
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    better formatting like this?

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  41. anonymous
    • one year ago
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    you have been soooo extremely helpful I wish i could thank you more!

  42. mathmate
    • one year ago
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    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!

  43. anonymous
    • one year ago
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    can you show me what the matrix would look like?

  44. anonymous
    • one year ago
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    I'm sorry I'm not very smart :(

  45. mathmate
    • one year ago
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    |dw:1433211807693:dw| Dont understimate yourself! :)

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

  47. mathmate
    • one year ago
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    0 -2 ... -1 -3... for all 4 points

  48. anonymous
    • one year ago
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    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?

  49. mathmate
    • one year ago
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    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.

  50. anonymous
    • one year ago
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    I'm just going to leave it like that and get half credit, thank you for your help.

  51. mathmate
    • one year ago
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    Sorry! :(

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