Author Topic: TRansformations  (Read 6302 times)

Offline joel

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TRansformations
« on: May 17, 2009, 12:03:22 pm »
How do i find the matrix which represents a transformation

Offline shan2391

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Re: TRansformations
« Reply #1 on: May 17, 2009, 12:05:37 pm »
i have the same problem refrence Q7b OCt08

zara

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Re: TRansformations
« Reply #2 on: May 17, 2009, 12:07:04 pm »
very simple....
first draw the unit matrix n den watevr matrix is given draw dat...n den chk wat kinda transformation is hppning between the unit matrix n the one given...

hope u get it.. :)

Offline shan2391

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Re: TRansformations
« Reply #3 on: May 17, 2009, 12:28:25 pm »
zara can u plzz solve the Q7b in oct08

Offline Ghost Of Highbury

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Re: TRansformations
« Reply #4 on: May 17, 2009, 12:37:39 pm »
first write down 2 sets of co-ordinates from triangle T in a matrix form
then multiply it with the unknown matrix and equate it to the matrix form of two corrseponding sets of co-ordinates of the image i.e R

(2   8 ) *   (w  y)     (-4  -4)
(4   4)      (x  z)  = (-2  -8)

therefore you can find the values of w,x,y and z by multiplying (-4  -4) with the inverse of (2  8 )
                                                                                      (-2  -8)                           (4  4)


=> so the answer is (0  -1)
                            (-1  0)

plz infrm me if u didn't understand...as i am available anytime in studentforums...
Good luck
« Last Edit: May 17, 2009, 12:39:46 pm by eddie_adi619 »
divine intervention!

Offline angell

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Re: TRansformations
« Reply #5 on: May 17, 2009, 12:39:53 pm »
im still confused:(
oh churiyaan charha dey..
oh mehndiya kara dey..
oh jhanjara pawan dey...
On the dance floor oh mundiye...Nach Baliye!

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Offline sweetsh

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Re: TRansformations
« Reply #6 on: May 17, 2009, 12:40:52 pm »
Your explanation is good!

Offline Priceless

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Re: TRansformations
« Reply #7 on: May 17, 2009, 12:46:46 pm »
hmmm shan2391 c u can du it da way zara or eddie_adi619 told or in our skul dey hv thot us da base vectors which r matrixes n represent da transformations. da only bad part is dat u hv 2 lern dem. du u want dem?
Don't say "God I have tooo many problems" but say "Problems I have God!"   Gud Luck 2 all 4 xams. Hope v all du well.....fingers crossed LOL

Offline reishamix

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Re: TRansformations
« Reply #8 on: May 17, 2009, 12:51:32 pm »
base vectors are life savers!!
and they dnt tke long to lern
5 minutes maximum...
gd fr my level ..
which isnt too high .. =P

Offline Ghost Of Highbury

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Re: TRansformations
« Reply #9 on: May 17, 2009, 12:52:19 pm »
@sweetsh - thanx a lot   :)
@angel - okk...so lets try the next sum

U onto Q

take any 2 co-ordinates of triangle U i.e = (-6,2) and (0,2)
arrange them vertically o form a 2 by 2 matrix

(-6  0)
(2   2)

now let say the unknown matrix of transformation is
(a  b)
(c  d)

so it implies that when you multiply the co-ordinates of U with the matrix of transformation, you get the co-ordinates of the image i.e triangle Q...(look at the corresponding co-ordinates of U in Q)
you can see that the point (-6,2) is mapped onto (-6,4) and (0,2) to (0,4)
soo the equation is

(-6  0)  *   (a  b)  = (-6  0)
(2   2)       (c  d)     (4   4)

if you take (-6  0)
                (2   2) to other side then it becomes the inverse...

so you multiply

(-6  0)                            (-6  0)
(4   4) with the inverse of  (2   2)

therefore u get the answer (1  0)
                                     (0  2)
divine intervention!

Offline shan2391

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Re: TRansformations
« Reply #10 on: May 17, 2009, 12:53:16 pm »
first write down 2 sets of co-ordinates from triangle T in a matrix form
then multiply it with the unknown matrix and equate it to the matrix form of two corrseponding sets of co-ordinates of the image i.e R

(2   8 ) *   (w  y)     (-4  -4)
(4   4)      (x  z)  = (-2  -8)

therefore you can find the values of w,x,y and z by multiplying (-4  -4) with the inverse of (2  8 )
                                                                                      (-2  -8)                           (4  4)


=> so the answer is (0  -1)
                            (-1  0)

plz infrm me if u didn't understand...as i am available anytime in studentforums...
Good luck
thanks eddie i got it rep for u.

Offline Ghost Of Highbury

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Re: TRansformations
« Reply #11 on: May 17, 2009, 12:54:28 pm »
hey thanks a lot shan....

@priceless and reishamix

i wud like to learn the base vectors method ..plzz.

it wud very kind of u to teach me..
thank you

divine intervention!

Offline Ghost Of Highbury

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Re: TRansformations
« Reply #12 on: May 17, 2009, 12:56:49 pm »
can someone plzz teach me base vectors..!!
divine intervention!

Offline reishamix

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Re: TRansformations
« Reply #13 on: May 17, 2009, 01:00:16 pm »
draw like a sketch of an axis
mark a point "i" wid de coordinates (1,0)
and "j" wid de coordinates (0,1)

thts the base vector...
theyr written like (1 0)
                       (0 1) like any coordinates

and whn they ask u to change the object into the transformation (0 1)
                                                                                        (1 0)
u simply change the coordinates on "i" and "j"
and u knw if its a reflection , rotation or wtevr!!

Offline reishamix

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Re: TRansformations
« Reply #14 on: May 17, 2009, 01:02:14 pm »
theyr easier to use
and very simple
i cant draw em here gimme ur email adress
and ill draw em on msn