In this critical part of the year, The Temple resembles a ‘United Nations’ of sorts – a mass gathering of ~~chatty~~ students representing the many schools of Singapore, coming together for a common cause as one united people, regardless of race, language or religion, so as to achieve their A1s and happiness and avoid scoldings by teachers and parents.

It’s also the period when the number of extra lessons increases, along with the probability of students from one class meeting those from another.

Take Student `J` and Student `T` for example, two conscientious, single & available, hot-blooded boys who had been diligently attending Miss Loi’s *joss sticks* sessions since time immemorial, who were eagerly anticipating their next class – one that was rumoured to have many *chio* girls in attendance.

Imagine their dismay when it turned out to be an all-boys’ class, with Miss Loi being the *chio*-est girl in the class.

As they swallowed their bitter disappointment and resigned themselves to the mundane maths questions on their desk, a crumpled piece of paper flew out suddenly from nowhere to hit them on the head.

Startled, they turned towards the direction of the missile, only to find their jaws dropping simultaneously at the sight of an absolute **stunner** of a girl, dressed in the most *kawaii* Sailormoon uniform, seated at the far corner of the room.

The long, flowing Pantene hair, an impish smile, and a wink from the almond-shaped eye of this suspected Japanese exchange student were all it took to divert their attention firmly away from the quadratic curves on the board to the curves of her slender body.

They were desperate to stem the bleeding from their noses now, as she pointed her finger teasingly to the crumpled pieces of paper on the floor, which they hastily picked up to discover the following message scribbled inside:

Hello Handsome!

Maths is soooo boring! I’m falling asleep! Can you please pass me some Sour Sweets from the jars on your desk?

The one who passes me the most Sour sweets will get a date with me tonight *wink*

And thus, as hot-blooded males in heat tend to do in these situations, they promptly discarded their BFF status and began grabbing sweets frantically from the jars, totally oblivious to the fact that, to the rest of the people in the class who couldn’t *see* this girl, Miss Loi was still the *chio*-est girl in the room.

Two jars containing a *mixture* of Sour and Cola sweets lie before Students `J` and `T` respectively.

As of now, both of them had made three *failed* attempts to pass sweets to the girl, for they were caught by Miss Loi each time they grabbed a handful of sweets from the jars (students at The Temple are allowed one sweet at a time for their own consumption only). All sweets taken from the jars were confiscated and never placed back into the jars.

The tables below show the number of sweets in each jar at the beginning, and the number of sweets taken out and confiscated by Miss Loi on each attempt.

Student J | Student T | |||
---|---|---|---|---|

Sweet Flavour | Sour | Cola | Sour | Cola |

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 |

Given that the number of sweets Student `J` has taken out on his three attempts is represented by the matrix `M` = , and that the same information for Student `T` is represented by a matrix `N`.

- Write down the matrix
`N`. - Given that
`L`= , calculate`J`=`L``M`and`T`=`L``N`. Describe what is represented by the elements of`J`and`T`. - Calculate
`K`=`L`(`M`+`N`), and describe what is represented by the elements of`K`. - Calculate −
`K`, and describe what is represented by the elements of −`K`. - If they both managed to take out
*all*the remaining sweets from the jars and pass them*all*to the girl on the 4th attempt (due to Miss Loi being in the toilet),**by comparing the relevant elements of two suitable matrices**, determine who gets to ‘date’ the girl. - A Sour Sweet costs $0.60 and a Cola Sweet costs $0.40. Write down two matrices such that the elements of their product under matrix multiplication will give the total cost of the sweets in each jar. Hence, find the total cost of the sweets in each jar.

Hope this *cheong hei* (ala long-winded) question will provide some practice on *Matrix Addition/Subtraction/Multiplication* in an *Application of Matrices in Solving Everyday Life Problems* for those of you studying for your O-Level EMaths now, though it’s not everyday you get the chance to go on a date with ~~Sadako~~ a pretty girl!

## 7 Comments

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

Miss Loi:Commencing conversion of your matrices into a more readable form ...1) =

NYes. Since

Mhas been defined as a 3x2 matrix for the sweets StudentJhas taken (the blue numbers in the table), we read off the relevant rows and columns for the matrixNfor StudentT(the green numbers in the table):JTTotal in jar at the start1st Attempt4102nd Attempt12223rd Attempt66Note 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=LMas defined in the question.So via a straightforward matrix multiplication,

J==

=

1x3 matrix × a 3x2matrix 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

JandTshows 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

JandTrepresents the total no. of sour (left column) and cola (right column) sweets taken out fromeachjar 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

cheemterm, if you recall from Sec One, meansA(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 frombothjars 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 jarsSuddenly, 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 thetotalno. 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 sometotalamount with elements that are greater than the respective ones inK, 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 ...

JTTotal in jar at the startAnd 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&Tin the final round. Mathematically speaking it's simply:From Part 2, we already have

J&Trepresenting the total sweets left in each jar after 3 attempts.And if one were open one's eyes

big bigthe total no. of sweets at the start is staring at you in the face from the first row of the table:JTTotal in jar at the startSo we can form and compare our matrices as follows:

JTNo. 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

leftcolumn of each matrix to find StudentJhas 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 asmultiplication 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 moand 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 moagain 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

orderof 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

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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 ^_^''

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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 comprehensionto 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 😉

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

*shows stern face*

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Hi Handsome

Nash!So sweet of you to solve the question!

Suddenly I don't feel like going out with

TorJanymore. I wanna go out with you!*wink*

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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

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