Lesson 4 of 8
What is a matrix?
A matrix is a rectangle of numbers. Learn rows, columns, size and how to name one entry.
The idea
A matrix is a rectangle of numbers arranged in rows and columns. Each number is called an entry. Matrices are usually named with capital letters.
Rows and columns
A row runs across, from left to right. A column runs down, from top to bottom. Matrix A has 2 rows:
- row 1 is 2, 7, 1
- row 2 is 5, 0, 3
and 3 columns: column 1 is 2, 5; column 2 is 7, 0; column 3 is 1, 3.
The size of a matrix
We describe the size as rows × columns, always rows first. A has 2 rows and 3 columns, so it is a 2×3 matrix (say “two by three”). A 3×2 matrix would be a different shape: 3 rows and 2 columns.
Naming one entry
To point at one entry we use a small letter with two numbers underneath. In a sub i j, the first number i is the row and the second number j is the column. Row first, then column, the same order as the size.
The highlighted entry is in row 1, column 2, so it is a sub 1 2 = 7. Similarly, a sub 2 1 = 5, because row 2, column 1 holds a 5. Notice that a12 and a21 are different entries.
Worked example
What is the entry a sub 3 1?
Read the subscript
a sub 3 1 means row 3, column 1.
Find the cell
A equals a 3 by 2 matrix, row 1: 4, 9; row 2: 6, 1; row 3: 8, 3Row 3, column 1 holds 8.
Common mistakes
- Columns first. Size and subscripts both put the row first.
- Counting entries instead of rows. A 2×3 matrix has 6 entries, but only 2 rows.
- Reading a21 as row 1, column 2. The first number is always the row.