To calculate costs with matrices, multiply a row of quantities by a column of matching unit prices. The resulting entry gives the total for that order at that supplier. Keep the items in the same order in both matrices.
The 2027 SEC G3 Mathematics K310 syllabus covers interpreting matrices and multiplying them where appropriate. This guide shows how to label the product so you can use it to make a purchasing comparison.
- Use one order per row of the quantity matrix.
- Use one supplier per column of the price matrix.
- Match each quantity to the price of the same item.
- Read the result using the order and supplier labels.
CHAPTER 1 OF 4 · Back to contents
Decide what the answer matrix will show
Suppose the rows of Q stand for two classes and its columns stand for notebooks, folders and pens. Let P have one row per item and one column per supplier. The shared item list is the reason the matrices can be multiplied in the order QP.
A 2 × 3 matrix times a 3 × 2 matrix gives a 2 × 2 matrix. The two outer numbers give the size of the result. Here that means two classes and two suppliers.
Write the labels even when both dimensions happen to be equal. A row of results is about a class, while a column of results is about a supplier.
CHAPTER 2 OF 4 · Back to contents
Worked example | Two classes and two suppliers
Class A orders 8 notebooks, 5 folders and 12 pens. Class B orders 6 notebooks, 9 folders and 10 pens. Supplier X charges $3, $2 and $1 respectively. Supplier Y charges $2, $3 and $1.
| Class | Supplier X | Supplier Y |
|---|---|---|
| A | 46 | 43 |
| B | 46 | 49 |
Class A with Supplier X costs 8 × 3 + 5 × 2 + 12 × 1 = 46 dollars. Use the same row with the second supplier’s price column to get 8 × 2 + 5 × 3 + 12 × 1 = 43 dollars.
The cheaper supplier depends on the order. A benefits from Y’s lower notebook price because it orders more notebooks than folders. B orders more folders than notebooks and does better with X.
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CHAPTER 3 OF 4 · Back to contents
Practise a shared order
If the two classes must choose the same supplier, add the values down each supplier column. X costs 46 + 46 = 92 dollars. Y costs 43 + 49 = 92 dollars.
You can check by combining the original quantities into a row of 14 notebooks, 14 folders and 22 pens. Both suppliers have the same total price for one notebook and one folder, so both give the same combined cost.
If the orders may be split and there are no extra fees, use Y for A and X for B. The total falls to 43 + 46 = 89 dollars.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Why do I multiply across one row and down one column?
Those entries pair the quantities for one order with the prices from one supplier, item by item.
Can I reverse the matrices?
PQ is a different product. Here it would have size 3 × 3 and would not represent class-by-supplier totals.
What if the supplier lists its prices in a different order?
Reorder the entries to match the item labels in the quantity matrix before multiplying.
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