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Discrete Mathematics/Computer Science
23. CC.HSA.REI.C.9
23.3 Matrix multiplication
Matrix Multiplication
Multiply matrices with the row-by-column rule: pair each row with each column, multiply, and add.
What You'll Learn
Matrix multiplication uses a row-by-column rule, not entry-by-entry.
Each product entry pairs a row with a column: multiply matching numbers and add.
Multiplication is defined only when inner dimensions match: (m x n)(n x p).
The product has size m by p.
Matrix multiplication is not commutative: AB is generally not equal to BA.
What You'll Practice
1
Computing dot products of n-tuples with matching lengths
2
Multiplying 2×2, 2×3, 3×3, and larger matrices using row-column multiplication
3
Multiplying matrices with different dimensions (2×1, 3×2, 4×2, etc.)
4
Identifying when matrices cannot be multiplied due to incompatible dimensions
Why This Matters
Matrix multiplication is essential for advanced mathematics, computer graphics, data science, and engineering. You'll use this skill in linear algebra, physics simulations, machine learning algorithms, and any field involving transformations and systems of equations.
Before You Start — Make Sure You Can:
This Unit Includes
12 Video lessons
Practice exercises
Learning resources
Skills
Matrix Multiplication
Dot Product
N-tuples
Linear Algebra
Dimension Compatibility
Row-Column Method
OH Curriculum Aligned