Have you ever seen a list of test scores arranged in a table? Or perhaps a team duty roster? Unconsciously, we often encounter data presented in rows and columns. Well, this arrangement of numbers or information in rows and columns is the basis of the matrix concept.
A matrix is a collection of numbers specially arranged in rows and
columns to form a rectangular array. The numbers that make up
this matrix are called matrix elements. Matrices are usually written
within parentheses () or square brackets [].
For example, consider the Math and English test score data for the following three students:
Student Name
Math Score
English Score
Aisyah
80
75
Alex
70
95
Wayan
95
75
The data above can be presented in matrix form. If we only take the numbers, the matrix will look like this:
A=807095759575
Or it can also be written with parentheses:
A=807095759575
In this example, the numbers 80,75,70,95,95,75 are the elements of matrix A.
In a matrix, there are several important terms you need to know:
Row: An arrangement of elements horizontally.
Column: An arrangement of elements vertically.
Matrix Element: Each number or entry within the matrix.
Let's look back at matrix A from the previous example:
A=807095759575
Row1 is [8075]
Row2 is [7095]
Row3 is [9575]
Column1 is 807095
Column2 is 759575
Matrix elements are usually denoted by a lowercase letter corresponding to the matrix name, with two indices, for example aij. The first index (i) indicates the row position, and the second index (j) indicates the column position.
So, for matrix A above:
a11 is the element in the 1st row, 1st column, which is 80.
a12 is the element in the 1st row, 2nd column, which is 75.
a21 is the element in the 2nd row, 1st column, which is 70.
a22 is the element in the 2nd row, 2nd column, which is 95.
a31 is the element in the 3rd row, 1st column, which is 95.
a32 is the element in the 3rd row, 2nd column, which is 75.
Every matrix has a size called its order. The order of a matrix is determined by the number of rows and columns it has. If a matrix has m rows and n columns, then the matrix is said to be of order m×n (read as "m by n").
Consider our matrix A again:
A=2 columns807095759575807095⎭⎬⎫3 rows
Matrix A has 3 rows (indicated by the curly brace on the right) and 2 columns (indicated by the curly brace below). So, the order of matrix A is 3×2. We can write it as A3×2.
Another Example:
Suppose we have student attendance data for one semester:
Student Name
Permitted
Sick
Unexcused
Aisyah
2
1
0
Alex
3
1
1
Wayan
1
2
1
If we convert this into matrix B:
B=3 columns231112011231⎭⎬⎫3 rows
Matrix B has 3 rows (indicated by the curly brace on the right) and 3 columns (indicated by the curly brace below). Thus, the order of matrix B is 3×3. We can write it as B3×3.
aij : Element of matrix A in the
i
-th row and j
-th column.
By understanding this basic concept, you are ready to learn more about the types of matrices and the operations that can be performed on them. Matrices are very useful tools in various fields, you know, from mathematics, physics, computer science, to economics!
