By: Miss Loi

Miss Loi — Thu, 22 Oct 2009 14:37:35 +0000

Nash, Miss Loi got scold you meh??? Sadako! Leave the NS boy alone! Shoo! Shoo!

By: Nash

Nash — Thu, 22 Oct 2009 13:16:29 +0000

Sorry Miss Loi, I will be more careful for future posts and my upcoming exams (bows head) and i will also learn syntex to make life easier for you.

It hurts more to be scolded by a person you never even see b4 (looks at censored sunday time paper) >_<

To Sadako
I don't mind, a ghost buddy will be useful when i go to Tekong in Feb. but come find me in Dec, AFTER my exams.

Bet u didn't expect that =P

By: Sadako Loi

Sadako Loi — Wed, 21 Oct 2009 09:50:26 +0000

Hi Handsome Nash! So sweet of you to solve the question! Suddenly I don't feel like going out with T or J anymore. I wanna go out with you! *wink*

By: Miss Loi

Miss Loi — Wed, 21 Oct 2009 05:16:44 +0000

Oh and, as some students would know, it's not really all fun and games at The Temple either.

*shows stern face*

By: Miss Loi

Miss Loi — Wed, 21 Oct 2009 05:14:54 +0000

Nash: Just completed the loooong marking of your workings.

Take heart that while wordy EMaths matrices questions tend to be a little, well, wordy, the underlying mathematics is usually very straightforward as (in the absence of AMaths stuff like determinants and inverse matrices) there's really nothing much they can ask in EMaths matrices, one simply has to do a bit of reading comprehension to understand the question fully before barging in.

P.S. It's not that difficult to 'draw' matrices in your comments (imagine even an IT-inept Miss Loi can do this!)

Refer to the syntax guide and you'll find this:
e.g. [ pmath ](matrix{row}{col}{1 2 ... elements})[ /pmath ].

Try it using the preview button below

By: Nash

Nash — Mon, 19 Oct 2009 13:14:17 +0000

Oh by the way Miss Loi, The maths department at my school (the video) comes up with whacky stuff only once in awhile its not really all fun and games there ^_^''

By: Nash

Nash — Mon, 19 Oct 2009 13:07:15 +0000

Cant draw matrices on this thing so please bear with it..

Miss Loi: Commencing conversion of your matrices into a more readable form ...

1) = N

Yes. Since M has been defined as a 3x2 matrix for the sweets Student J has taken (the blue numbers in the table), we read off the relevant rows and columns for the matrix N for Student T (the green numbers in the table):

Sweet Flavour	Sour	Cola	Sour	Cola
	Student `J`		Student `T`
Total in jar at the start	40	25	24	48
1st Attempt	14	18	4	10
2nd Attempt	10	0	12	22
3rd Attempt	4	2	6	6

Note that data in the first row (with info on the total sweets in the jars) to not used to form the matrix in this part. Please always read such long-winded questions carefully to avoid reading off the wrong rows/columns.

2)
J =

Yes, J=LM as defined in the question.

So via a straightforward matrix multiplication,
J =
=
=

(recall that a 1x3 matrix × a 3x2 matrix will result in a 1x2 matrix i.e. no. of cols in 1st matrix x no. rows in 2nd matrix)

T =

Similarly, T=LN
=
=
=

Matrices J and T shows the total no. of cola and sour sweets taken by students J and T ( and confiscated by Miss Loi)

Yes. From the table in the question, you'll see that J and T represents the total no. of sour (left column) and cola (right column) sweets taken out from each jar in the three attempts.

3) The inter-mediate step are too hard to type for this part so ill just give the final answers.
K = (50 54 58) → No workings leads to careless mistake!

K=L(M+N)
=
=
=
=

OR if you trust your own answers and feelings from Part 2 ...

Since matrix multiplications are distributive (basically this cheem term, if you recall from Sec One, means A(B+C) = AB+AC),

K=L(M+N) = LM+LN
= J+T (from part 2)
=
=

And since K = J+T, it represents the total no. of sour (left column) and cola (right column) sweets taken out from both jars in the three attempts.

4) (64 73) - (50 54 58) = (14 19 15)
→ careless mistake cascaded from Part 3
(14 19 15) represents the no. of cola and sour sweets left in the jars

Suddenly, an alien matrix with two alien numbers (64 and 73) not found in the table hovers in the question to strike fears into us earthlings.

But if you stop and take a deep breath, you'll realize that we're trying to subtract K, which is the total no. of sweets taken from both jars, from this alien matrix. As such, we may instinctively deduce that this matrix must have something to do with some total amount with elements that are greater than the respective ones in K, since we shouldn't have any negative elements here.

So we look to the row of data that hasn't yet been utilized in this question ...

Sweet Flavour	Sour	Cola	Sour	Cola
	Student `J`		Student `T`
Total in jar at the start	40	25	24	48

And viola ... 40+24=64 (total no. of sour sweets in both jars) and 25+48=73 (total no. of cola sweets in both jars)!
⇒ (64 73) − (50 58) = (14 15) ⇒ the no. of cola and sour sweets left in the jars

5)
Total no. of sweets given to the girl by J
= 40 + 25 - 14 - 10 - 4 - 18 - 2
=17
Total no. of sweets given to the girl by T
= 24 +48 -12 - 4 - 6 - 6 - 22 -10
=12
Since student J gave more sweets to Sadako than student T, J get the right to date Sadako. Good luck with that ^_^''

And so we come to the dreaded part in EMath matrix questions that requires you to form your own matrices.

We wish to know how many sweets (specifically Sour sweets) that was passed to the girl by Students J & T in the final round. Mathematically speaking it's simply:

Total sweets in each jar at the start − total sweets taken out in three attempts

From Part 2, we already have J & T representing the total sweets left in each jar after 3 attempts.

And if one were open one's eyes big big the total no. of sweets at the start is staring at you in the face from the first row of the table:

Sweet Flavour	Sour	Cola	Sour	Cola
	Student `J`		Student `T`
Total in jar at the start	40	25	24	48

So we can form and compare our matrices as follows:

	Student `J`	Student `T`
No. of sweets passed to girl	(40 25) − `J` = (40 25) − (28 20) = (12 5)	(24 48) − `T` = (24 49) − (22 38) = (2 10)

And since Sadako loves Sour sweets in the story (ok should've included this in the question proper), we compare the left column of each matrix to find Student J has given more Sour sweets (12 vs 2) to 'win' her heart!

5)
(0.6)
(0.4) = X
Cost of sweets = (64 73)X [must be multiplied in this order]
=$67.60

Again, we say this aloud:

Total cost of sweets in each jar
= Cost per sweet × Total no. of sweets in jar OR
= Total no. of sweets in jar × Cost per sweet

Once you've confirmed to yourself that the above statement makes sense, you go about 'creating' your matrices:

Cost per sweet:
OR
Total no. of sweets in jar:
OR

So which matrix do you use for your product expression? IT DOESN'T MATTER as long as multiplication is possible (i.e. no. of cols in left matrix = no. of rows in right matrix) AND make sure you check that you're multiplying the right elements.

So, say, should you einee menee minee mo and select and and you put them in this order:

, you'll find that they can't multiply at all
⇒ FAIL

But if you switch them around:

=
(CHECK that you're multiplying 0.60 with Sour sweets and 0.40 with Cola sweets!)
=
⇒ YAY!

On the other hand, if you einee menee minee mo again and select and you can get lucky if you put them in this order:

⇒ they can multiply!
=
(CHECK again that you're multiplying 0.60 with Sour sweets and 0.40 with Cola sweets!)
=
⇒ DOUBLE YAY!

You're get the same final answer but note that the order of the final matrix is different!

Hopefully Sadako will let me go for not solving the triangle question now o_o...Thanks in advance Miss Loi, I am not IT savvy enough to put matrices in my post

By: Miss Loi

Miss Loi — Sun, 18 Oct 2009 07:49:30 +0000

Meet the prettiest girl at The Temple: http://bit.ly/1aToMR

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