Definition of Matrix
A matrix is an arrangement of numbers, variables, or expressions in rows and columns forming a rectangular or square array.
Why Matrices Are Important
- Organize data clearly
- Solve multiple equations together
- Used in science, engineering, economics, and computer graphics
Matrix Notation
Matrices are represented by capital letters such as A, B, or M. The element in the i-th row and j-th column is written as a_{ij}.
Examples of Matrices
Matrix with 2 rows and 3 columns:
Square matrix (same number of rows and columns):
Types of Matrices
- Row Matrix – one row
- Column Matrix – one column
- Square Matrix – rows = columns
- Zero Matrix – all elements are zero
- Identity Matrix – diagonal elements are 1
Matrix Operations
Addition and Subtraction
Matrices can be added or subtracted only if they are the same size. Each element is added or subtracted with its corresponding element.
Scalar Multiplication
Every element in the matrix is multiplied by the same number.
Matrix Multiplication
Matrix multiplication is possible only when the number of columns in the first matrix equals the number of rows in the second matrix.
Matrix multiplication is not commutative: A \times B ≠ B \times A
Video Example: Multiplying Matrices
Solved examples
Profit = Revenue − Cost
Correct Answer: A
Common Mistakes
- Adding matrices of different sizes
- Multiplying matrices in the wrong order
- Mixing up rows and columns
Summary
A matrix is a powerful way to organize and calculate data. By following simple rules, matrices help solve complex problems efficiently.