SKEDSOFT

Maths For Engineers - 1

Scalar Multiplication:

Let A = [ aij] m\times \!\,n 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 = [ Cij] m\times \!\,n where Cij = r aij for all i and j.

Example:

Properties of Scalar Multiplication:

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:

Dot Product:

The Dot Product A.B of a 1 \times \!\, n row vector

 

and an n \times \!\, 1column vector

  

is defined as;

Example:1