A matrix (plural: matrices) is a rectangular arrangement of numbers, symbols, or expressions that are organized in rows and columns, and enclosed by brackets.
Each number in a matrix is called an \(\textbf{entry}\) or \(\textbf{element}\text{.}\) The position of each element is identified by its row number and column number.
Subsection2.1.1Identifying a Matrix in Different Situations
A \(\textbf{matrix}\) is a way of organizing numbers or information in rows and columns—just like the tables you have seen in other topics, such as measurement and data handling. Matrices help us organize, compare, and analyze data efficiently.
Matrices are powerful tools for organizing and analyzing real-world data, such as sports scores, business sales, or scientific results. By turning tables into matrices, we can use mathematical methods to solve problems more easily.
The Greenfield School Cafeteria prepares meals for students in three school levels: Lower Primary, Upper Primary, and Secondary. Each week, they prepare two types of meals: Vegetarian and Non-Vegetarian. The number of meals prepared (in hundreds) for Week 1 and Week 2 is recorded in the tables below:
We compare the Term 2 column: Alice = 5, Brian = 6, Carol = 4. The highest number is \(\textbf{6}\text{,}\) which belongs to \(\textbf{Brian}\text{.}\)
Subsection2.1.2Determining the Order of a Matrix in Different Situations
The order of a matrix tells us how many rows and columns it has. This is written as rows × columns (for example, 2 × 3 means 2 rows and 3 columns). Knowing the order helps us describe, compare, and use tables and schedules correctly in real life.
The order of a matrix helps us describe and use tables, schedules, and data sets correctly in real life. It tells us how much information a matrix can hold.
Subsection2.1.3Determining the Position of Items in a Matrix in Different Situations
Every number or item in a matrix has a special place, just like a seat in a classroom or a product on a shelf. We use the row and column numbers to find the exact position of each item. This helps us quickly locate information in tables, scoreboards, or lists.
Imagine a 3×3 matrix representing a simple map. Each cell can have a value: 0 (empty), 1 (tree), 2 (house), 3 (treasure). The map is represented by the following matrix:
Subsection2.1.4Determining Compatibility of Matrices in Addition and Subtraction
In real life, we often want to combine or compare data from different sources—like adding up sales from two weeks or comparing scores from two rounds of a game. To do this with matrices, the data must be organized in the same way. This means the matrices must have the same number of rows and columns (the same \(order\)).
The table below shows the number of books borrowed from a library by three students (Alice, Brian, and Carol) in two different months, and then in two more months.
You can only add or subtract matrices if they have the same order (the same number of rows and columns). This allows us to combine or compare real-life data correctly.
Subsection2.1.5Carry Out Addition and Subtraction of Matrices in Real Life Situations
In everyday life, we often need to combine or compare data from different sources—such as adding up scores from two football matches or finding the difference in sales between two weeks. Matrices make these calculations easy and organized!
Use the GeoGebra applet below to practice adding and subtracting matrices. You can choose either 2×2 or 3×3 matrices, enter your own values, and select the operation (addition or subtraction).
\(A - B\) shows the difference in sales between Vendor 1 and Vendor 2 for each fruit and day. A negative number means Vendor 2 sold more of that item than Vendor 1.
Subsection2.1.6Reflecting on the Use of Matrices in Real Life Situations
Matrices are everywhere in our daily lives! Whenever you see a table, a timetable, or a chart, you are looking at data that can be organized as a matrix. Matrices help us organize, compare, and analyze information quickly and clearly.
The local sports club keeps a matrix of scores for three teams (Lions, Tigers, Eagles) over four games. The club wants to know which team performed best overall and in which game the highest score was recorded.
