Matrix Addition and Subtraction

According to the dictionary, matrices are "rectangular arrays of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules". Matrices are used for mapping, engineering, and population modeling, among many other ways.

We generally use capital letter as the variable for a matrix. The capital letter may further contain a subscript of the form (a x b), where a is the number of rows in the matrix, and b is the number of columns. For example A_(2x3) would be a matrix with two rows and three columns.

Each entry in a matrix can also be referenced by a subscripted variable. In the case of the matrix A, we refer to the top left cell as a_1,1 because it is the first row, first column of the matrix A. Likewise, a_1,2 = 2x and a_2,3 = 1.

Rules for matrix addition:

1. Matrices that are to be added together must be the same size (same number of rows and same number of columns)
2. The corresponding cells of each matrix are added together. So cell a_1,1 is added to cell b_1,1, cell a_3,2 is added to b_3,2, and so on.

Note that matrix addition is commutative, so A + B = B + A

Example:

Rules for matrix subtraction:

1. Matrices that participate in a subtraction must be the same size (same number of rows and same number of columns)
2. The corresponding cells of each matrix are subtracted. So if we have A - B, then cell b_1,1 is subtracted from cell a_1,1, cell b_3,2 is subtracted from a_3,2, and so on. Every cell must participate in the subtraction.
   

Note that matrix addition is not commutative, so A + B ≠ B + A

Example:

How to do matrix multiplication
Creating a population growth matrix