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=LM and T=LN. 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!
