From a marks table…
| Student | Maths | English |
|---|---|---|
| Tariro | 78 | 81 |
| Tawanda | 65 | 74 |
| Chipo | 92 | 88 |
🌱 Start Here: What Is a Matrix?
A matrix is a rectangular arrangement of information in rows and columns. It is useful because a large table of numbers can be stored, compared and calculated with as one organised object.
…to a matrix
Remove the labels→788165749288
The position of every number still carries meaning.
Rows and columns
258417
The horizontal lines are rows. The vertical lines are columns.
Order of a matrix
rows × columns
258417is 2 × 3
Always count rows first.
Think Like a Mathematician: A 3 × 2 matrix and a 2 × 3 matrix both contain six entries. Why are they not the same order?
🎯 Learning Objectives
- define a matrix;
- identify rows, columns and entries;
- state matrix order;
- use entry notation;
- connect matrices to real data.
Introduction
This lesson develops Introduction to Matrices from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
What Is a Matrix?
A matrix is a rectangular arrangement of numbers or quantities written in rows and columns. Each value occupies a fixed position called an entry.
Order is rows × columns—not columns × rows.
Rows, Columns and Order
A= 2 5 −1 4 0 7
A has 2 rows and 3 columns, so its order is 2×3.
Rows
Horizontal arrangements. Row 1 is 2, 5, −1.
Columns
Vertical arrangements. Column 2 is 5, 0.
Entry Notation
aᵢⱼ means row i, column j. Here a₂₃=7.
Practice Questions
- State the order of a matrix with 4 rows and 2 columns.
- Find a₁₂ and a₂₁ above.
- How many entries are in a 3×5 matrix?
✅ Check Your Work
Show answers and working
- 4×2.
- a₁₂=5 and a₂₁=4.
- 15 entries.
🧩 Interactive Matrix Builder
📘 Remember
Key idea
The order of a matrix is always rows × columns. Entry aᵢⱼ is found in row i and column j.
⚠️ Common Mistakes
Do not reverse the order. A matrix with 2 rows and 3 columns is 2×3, not 3×2.
⭐ Exam Tips
Before doing any operation, write the order of every matrix. This quickly shows whether the operation is allowed.
🌍 Did You Know?
Matrices organise information in computer graphics, spreadsheets, transport networks and data science.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.