Operations with Matrices

You can represent matrices in any of the following:
1) A matrix can be denoted by an uppercase letter such as,
A, B, C, . . .

2) A matrix can be denoted by a representative element enclosed in brackets, such as,

3) A matrix can be denoted by a rectangular array of numbers.

Equality of Matrices: 
If two matrices A= (Aij) and B= (Bij) have the same size mxn and Aij = Bij ; then A=B. 

*It is important to know the size of your matrices so that you'll know whether you can perform the operation or not. 

*Matrices A and B are not equal because they have different sizes. Also with Matrices C and D, only if 
x = 3. 








* Column Matrix or Column Vector
A matrix with only 1 column. 

*Row Matrix or Row Vector
A matrix with only 1 row. 

MATRIX ADDITION
*You can only add matrices of the same size by adding their corresponding entries.  

Definition of a Matrix Addition: 
If A = (aij) and B = (bij) are matrices of size m x n, then their sum is the m x n matrix given by A + B = (aij+ Bij). 

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).