VG3
linear-algebra
Quiz
What are matrices?
A matrix is a rectangular array of numbers arranged in rows and columns — a powerful tool in linear algebra.
A matrix is a rectangular table of numbers. Matrices are used to represent systems of linear equations, geometric transformations and much more.
A = [a b] — 2×2 matrix
[c d]
[c d]
Matrix addition
[1 2] + [5 6] = [6 8]
[3 4] [7 8] [10 12]
Matrix multiplication
[1 2] · [5 6] = [19 22]
[3 4] [7 8] [43 50]
Important: Matrix multiplication is NOT commutative!
A · B ≠ B · A (in general)
A · B ≠ B · A (in general)
Applications: Matrices are used to solve systems of equations, describe 3D rotations, quantum physics, machine learning and much more!
Matrices are the Swiss army knife of mathematics — they solve almost everything.
— Arthur Cayley (1821–1895)
🧠 Test yourself
Question 1 of 5
What is a 2×3 matrix?