A matrix is a rectangular array of numbers which can be used to hold quantitative information (for example our water volumes or data volumes) in a structured way. Each number inside the matrix is known as an element of the matrix. Matrix mathematics can become quite complicated so this section here will serve to be just an introduction showing how simple matrices can be manipulated.


Here's an example of a simple matrix:



This is an example of a matrix with 4 elements, arranged in 2 rows and 2 columns. Matrices do not have to be square, they can be vertically rectangular, horizontally rectangular and of virtually any size although for the purposes of this section while deliberately restrict the size of the matrix because the arithmetic can become complicated with larger examples.



Here are 2 more matrices, the first one is a "2 x 2" matrix and the second one is a "2 x 1", they are numbered "rows x columns". 

Two matrices sitting side-by-side like these examples implies that they will be multiplied. There are many arithmetic operations that can be carried out on matrices (including of course multiplication) but there are rules which must be followed because not all arithmetic operations can be performed on all matrices, that is the matrices have to conform to certain rules (usually regarding structure) before they can be operated on in any particular arithmetic way.