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Maths, Addmaths and Statistics: Post your doubts here!

Dukeofwin

Dukeofwin

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ashiqbal said:
ok guys i am really sorry, i should have given the method that i use for transformation matices over here earlier. though i didnt know how to explain it!
This is more of a sort of a lesson than an actual mnemonic, with tips to memorise the matrices step by step and easily. There might be other mnemonics, but you will mix those all up during the exam and then you are dooomed!
View attachment 11839
so basically, what you need to learn at first that those with the yellow go about the pattern(the small circles are zeroes! :)):
(x.....0
0.....y)
and those with red go with the pattern:
(0......x
y......0)
These two samples are important to learn before you proceed forward! Remember that yellow ones resemble an identity matrix, while red doesnt. (a small mnemonic here: yellow chicks (choozay) are identical)
Those in Red will be Reflection along y=x and y=-x and Rotation of anticlockwise 90 degrees and clockwise 90 degrees
Rotating REXY is Red (where ReXY means REflection along Y=X)
now that we know which are red, lets learn the method of memorising these four matrices:

REFLECTION ON Y=X
this is simple, all positive, so (0 1 / 1 0) the slash means next line. the x coordinate becomes y coordinate and vice versa

REFLECTION ON Y=-X
now there is a negative sign here, which means that we will put a negative sign with all the members (0 -1 / -1 0) here, the x coordinate becomes negative y coordinate and the y coordinate becomes negative x coordinate.

ROTATION OF 90 degrees CLOCKWISE:
This is Clockwise rotation, right? so remember that we cant go in the opposite direction, so the negative sign on the left shows the restriction of rotating left(anticlockwise) and the positive 1 shows that we can rotate right(clockwise) (0 1 / -1 0)

ROTAION OF 90 degrees ANTICLOCKWISE:
you can guess that this time we are allowed to rotate left, so there will be a positive sign on the left(anticlockwise) and a negative sign on the right(clockwise). Guess the matrix now before looking up on the page to see it!

YOU MUST REMEMBER THAT WE CANNOT MOVE IN DIRECTION OF NEGATIVE SIGN IN ROTATION!

All the others follow the Yellow pattern.
the thing about those following the yellow pattern is that they are like Identity matrix, with only one member changed. if the number that is changed is the first member eg (x 0 / 0 1) then it means that the value of x is changed and if the number changed is last ie (1 0 / 0 y) then it means that the value of y has changed. so basically what u have to see is which value is changing.

In Reflection along the axes, the values are not actually changed, but their signs are changed.

Reflection Along X AXIS:
In this, the value of x remains the same, while y changes, right? when you flip the whole image upside down, the Y becomes -Y and the -Y becomes Y. so actually to change the sign of y, what will we do? yup we will change value of Identity matrix so that the last one becomes negative. (1 0 / 0 -1). Multiply any coordinate with this and the value of only y will become negative.
Reflection Along Y AXIS:
again the same thing happens, with value of x changing as we invert the image laterally(right to left). the sign of X changing means that the first member will change its sign. (-1 0 / 0 1)

Rotation of 180 DEGREES:
this is not actually a rotation, it is a reflection of both x and y coordinates at the same time. Therefore, both the above conditions would be applied and the matrix would become (-1 0 / 0 -1)

STRETCH Parallel to X AXIS:
in Stretch, the value of x changes while the value of y remains the same (IT is PARALLEL to X AXIS) so what wil we do to the identity matrix this time? Surely, because we have to change the value of x, we will change the first member, but what will we replace it with? This time there is SHEAR Factor involved, and that will take place of the x axis. if shear factor is k, then the matrix will become (k 0 / 0 1) (remember that only the first member is changed)
STRETCH Parallel to Y AXIS:
What is your guess for the transformation matrix? i will let you work this out on your own. Check your matrix with the one given in the pic.

ENLARGEMENT:
This is the simplest of all! You just multiply the identity matrix with the enlargement factor, k(1 0 / 0 1) so it becomes
(k 0/0 k)

those given in green, the shear matrices are quite difficult to understand so i suggest that you just memorise those two, that is what i have done.

the method of learning the matrices is quite enjoyable, and even if you forget the matrices, you can just work them out in the examination hall in seconds! and the thing is, once you understand this method, it becomes very difficult to forget!

I am tagging some of the people i remember now, if u know others, please tag them as well!
Rimsa, a.abid Spidey21 syed1995 MustafaMotani khizer shahab SalmanPakRocks scouserlfc Mayedah asd
Click to expand...
(a small mnemonic here: yellow chicks (choozay) are identical)! So freaking funny! Do you think everyone here thinks negatively?
Bracket things was super funny!
 
ashiqbal

ashiqbal

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Dukeofwin said:
(a small mnemonic here: yellow chicks (choozay) are identical)! So freaking funny! Do you think everyone here thinks negatively?
Bracket things was super funny!
Click to expand...
yar i have to look at every aspect before i can post any content here. Once i have suffered by not clarifying what i meant, will never make the same mistake again.
 
Haris Bin Zahid

Haris Bin Zahid

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asd: Thnx for all the help man! You surely are really knowledgeable and cooperative (MashaAllah).
Well....here is another question: The speed v m/s of a particle travelling from A to B, at time t s after leaving A, is given by v=10t-t^2. The particle starts from rest at A and comes to rest at B. Show that the particle has a speed of 5 m/s or greater for exactly 4√5 s.
Using 10t-t^2.=5, we get 5+2√5 and 5-2√5. The examiner report says to subtract one from the other. Why to do so?:(
 
Dukeofwin

Dukeofwin

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ashiqbal said:
yar i have to look at every aspect before i can post any content here. Once i have suffered by not clarifying what i meant, will never make the same mistake again.
Click to expand...
I understand it mate, Its just that it brought a smile to my face reading it so decided to post it.;)
Btw how long did it take you to type all that?
 
ashiqbal

ashiqbal

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beeloooo said:
Spidey21 do u knw about the planes of symmetry ?? can u give any idea about it !! check this out !!
http://clickpapers.net/past papers/math-/4024_s06_qp_1.pdf

q.16 part a !!

how is its answer = 7 ? :O
Click to expand...
first we have 6 planes of symmetry from the top of the prism where there is a hexagon, right? the planes of symmetry are those planes, like paper sheets, which divide the two parts equally so as they are symmetrical, meaning two prisms are produced with two three sided faces each
there is another plane of symmetry in the middle of the prism, where when we cut it, two cylinders of hexagonal faces are produced
add up those and that will be 6+1 = 7 :)
 
Spidey21

Spidey21

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ashiqbal said:
first we have 6 planes of symmetry from the top of the prism where there is a hexagon, right? the planes of symmetry are those planes, like paper sheets, which divide the two parts equally so as they are symmetrical, meaning two prisms are produced with two three sided faces each
there is another plane of symmetry in the middle of the prism, where when we cut it, two cylinders of hexagonal faces are produced
add up those and that will be 6+1 = 7 :)
Click to expand...
true
 
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