In mathematics, a matrix is an array of numbers arranged in rows and columns. We generally use matrices to represent one or more equations to simplify their solution.
A matrix is made up of elements within those rows and columns. Understanding placement helps the progression into operations on matrices, such as addition, subtraction, scalar multiplication, dot products, and inverses.
In the following example we see a 3×3 matrix. We label the dimensions of a matrix as rows X columns. Each number in a matrix is an element. In the general matrix, we see each element also has a corresponding position named just as the matrix was named, rows X columns.
We are able to perform operations on matrices as long as their dimensions align. Different operations require a different alignment of dimensions. You will see more of these operations in the proceeding sections.