Matrix operations

Math

Definition

The basic operations performed on matrices including addition, subtraction, scalar multiplication, and matrix multiplication. Matrices must have compatible dimensions for addition/subtraction (same size) and multiplication (columns of first = rows of second).

How It Works

  1. For addition/subtraction: add or subtract corresponding entries (matrices must be same size).
  2. For scalar multiplication: multiply every entry by the scalar.
  3. For matrix multiplication: take the dot product of each row of the first matrix with each column of the second.
  4. The result of multiplying an m×n matrix by an n×p matrix is an m×p matrix.

Examples

  • Adding two 2×2 matrices by adding corresponding entries
  • Multiplying a matrix by 3 (scalar multiplication)
  • Multiplying a 2×3 matrix by a 3×2 matrix to get a 2×2 result

Study This Concept

Practice matrix operations with free review games in these units: