# Scalar Multiplication

**Scalar Multiplication:**

Let A = [ a_{ij}] _{mn }and r be a real number. Then the Scalar Multiplication of the matrix A and the scalar r is a matrix C such that C = [ C_{ij}] _{mn }where C_{ij }= r a_{ij} for all i and j._{ }

**Example:
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**Properties of Scalar Multiplication:
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Let r and s be real numbers and A and B be matrices, then

1. r (sA) = (rs) A

2. (r s)A = rA sA

3. r (A B) = rA rB

4. A (rB) = r(AB) = (aA)B

**Example:
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**Dot Product:
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The Dot Product A.B of a 1 n row vector

and an n 1column vector

is defined as;

**Example:1
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