Matrices

Definition of Equality of Matrices
Two Matrices A = [aij] and B = [bij] are equal if they have the same size (m x n) and aij = bij
for i and j are less than or equal to m but greater or equal to one.

Matrix Addition
If A = [aij] and B = [bij] are matrices of m x n, then their sum is the m x n matrix given by
                     A + B = [aij + bij]
The sum of two matrices of different sizes is undefined.
Examples

Scalar Multiplication
If A = [aij] is an m x n matrix and c is a scalar, then the scalar multiple of A by c is the m x n matrix given by
          cA = [caij]
Example

Matrix Multiplication