Problem 51 - College Algebra

Question

What is a matrix?

Step-by-Step Solution

Answer

A matrix is a rectangular array of numbers. These numbers are also known as elements or entries of the matrix. Matrices are mainly used in fields such as computer graphics, physics, and engineering to represent and solve systems of linear equations.

Step 1: Definition

A matrix is a rectangular array of numbers or other mathematical objects, for which operations such as addition and multiplication are defined.

Step 2: Representation

Matrices are usually represented in the following way: each number inside of the array is called an element or an entry of the matrix. These entries are located by their position with respect to the rows (horizontal) and columns (vertical). For instance, a 2x2 matrix has 2 rows and 2 columns, which yields this general representation: \[ \begin{pmatrix} a & b \ c & d \end{pmatrix} \]. Here the variables \(a, b, c, d\) represent the elements of the matrix.

Step 3: Application

Matrices are applied in various fields of mathematics such as linear algebra, geometry, calculus and more. They are used to represent systems of linear equations, perform linear transformations, and model real-world problems in physics, engineering, computer graphics, among others.