Matrices
Matrices are rectangular arrays used to organise and transform data.
About this topic
A matrix is a rectangular array of numbers arranged in rows and columns, and its size is given as rows × columns. You add matrices of the same size entry by entry, multiply by a scalar by scaling every entry, and multiply two matrices with row-by-column dot products, which requires compatible sizes.
Matrix multiplication is not commutative. Matrices store data, solve systems of equations, and describe transformations in computer graphics and game engines.
Worked example: A is 2 by 3 with rows (1, 2, 3) and (4, 5, 6), and B is 3 by 2 with rows (1, 0) and (0, 1) and (2, 2). The product AB is 2 by 2. Its top left entry is 1·1 + 2·0 + 3·2 = 7. Matching inner sizes (3 and 3) allows multiplication, and the outer sizes give the result's size. A single matrix can store a table of sales by store and month, and multiplying by a price vector gives total revenue.
Image editing, video games and search engines use matrices to rotate, scale and transform. The biggest trap is assuming AB = BA; even when both exist they usually differ. Another is multiplying entries in matching positions instead of using row by column. Practice by finishing the check on sizes first, then computing entries one at a time. The identity matrix acts like the number 1.
Key ideas
- Rows × columns gives the size
- Add matching entries
- Multiply row by column
Quick check
Use cases: where Matrices helps
- Homework: review the key idea behind Matrices before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Matrices without notes.
- Visual learning: play with the interactive lab to see how Matrices changes when you adjust its inputs.
- Teaching a friend: explain Matrices in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Matrices?
Matrices are rectangular arrays used to organise and transform data.
What will I learn in Matrices?
Rows × columns gives the size. Add matching entries. Multiply row by column.
Is Matrices part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Matrices lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Matrices?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.