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Multiplying a Real Number by an Array


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 bij = xaij:

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

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