Scalar Multiplication of Matrices

In matrix algebra, a real number is called a scalar.

The scalar product of a real number, r, and a matrix A is the matrix rA. Each element of matrix rA is r times its corresponding element in A.

Given scalar r and matrix

Example 1:

Let A =

, find 4A.

Properties of Scalar Multiplication:

Let A and B be m × n matrices. Let O_m _× _n be the m × n zero matrix and let p and q be scalars.

Properties of Scalar Multiplication
Associative Property	p(qA) = (pq)A
Closure Property	pA is an m × n matrix.
Commutative Property	pA = Ap
Distributive Property	(p + q)A = pA + qA p(A + B) = pA + pB
Identity Property	1 · A = A
Multiplicative Property of –1	(–1)A = –A
Multiplicative Property of 0	0 · A = O_m _× _n

http://hotmath.com/hotmath_help/topics/scalar-multiplication-of-matrices.html

Rules for matrix addition:

Matrices that are to be added together must be the same size (same number of rows and same number of columns)
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: