A matrix is written as a grid of numbers with brackets on either side and represents a linear mapping between an input space and an output space. When referring to the dimensions of the matrix, the convention is to say the number of rows followed by the number of columns. For example, the matrix shown below would be called a “2 by 3” matrix because it has two rows and three columns.

The matrix notation is shorthand for a system of linear equations. So if you consider the matrix below which represents a linear mapping between the vector and the vector .

This can also be written as a system of linear equations like so: