Given a real number **x** and an array **THE** of type m x n, the product of **x** per **THE** it's a matrix **B** of the type m x n obtained by multiplying each element of **THE** per **x**, ie b_{ij} = xa_{ij}:

B = x.A |

Note the following example:

## Properties

Being **THE** and **B** arrays of the same type (m x n) and **x** and **y** any real numbers are worth the following properties:

a) associative: x. (yA) = (xy). THE

b) distributive of a real number in relation to the addition of matrices: x. (A + B) = xA + xB

c) distributive of a matrix with respect to the addition of two real numbers: (x + y). A = xA + yA

d) neutral element: xA = A, for x = 1, ie A = A

Next: Matrix Multiplication