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.
, find 4A.
Properties of Scalar Multiplication:
Let A and B be m × n matrices. Let Om × 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 = Om × n |
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