What Is a Matrix?
In mathematics, a matrix is a rectangular array or grid of numbers, symbols, or expressions arranged in rows and columns. It's a fundamental tool used to organize, store, and manipulate data in a structured format. Each item within a matrix is called an element or an entry.
Section 2: Rows, Columns, and Dimensions
The key components of a matrix are its rows (the horizontal lines of elements) and columns (the vertical lines of elements). The size or dimension of a matrix is described by its number of rows and columns, typically written as 'rows × columns'. For example, a matrix with 2 rows and 3 columns is called a '2x3' matrix.
Section 3: A Practical Example
Consider a 2x3 matrix named A. It might look like this: A = [[1, 9, -2], [4, 5, 0]]. This matrix has two rows and three columns. The element in the first row and second column is 9, and the element in the second row and first column is 4.
Section 4: Why Are Matrices Important?
Matrices are essential in many fields, including computer graphics, physics, engineering, and data science. They are used to solve systems of linear equations, represent geometric transformations like rotations and scaling, and efficiently process large datasets, such as in image processing or machine learning algorithms.