Paper 4: Fundamentals of Business Mathematics & Statistic

2.58 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

6. Unit (or Identify) Matrix
   A diagonal matrix having each diagonal element equal to one is called unit matrix. It denote by In.
   Thus,

2 3

1 0^100

I 0 1, I 0 1 0

0 0 1

= =^

(^)

7. Null (or Zero) Matrix
   A matrix of order m x n having all elements zero is called Null matrix and it’s denoted by 0.
   i.e.

2 x 3 3 x1 2 x 2

0 0 0^0 0 0

0 0 0 , 0 , 0 0

0

     

     

     

  

8. Upper Triangular Matrix
   A square is said to be an upper triangular matrix if all elements below the main diagonal are zero.
   As,

3 x 3 4 x 4

1 2 3 1 2 3^4

0 4 5 ,^0 5 6^7

0 0 6 0 0 8^9

0 0 0 10

   

   

   

   

   

 

9. Lower Triangular Matrix
   A square matrix is said to be an lower triangular matrix if all elements above the main diagonal are zero.
   i.e.

3 x 3 4 x 4

1 0 0 a 0 0 0

2 4 0 , b e 0 0

3 5 6 c f h 0

d g i j

OPERATIONS ON MATRICES

Equality of Matrices

Two matrices are said to be equal if they are of same order and their corresponding elements are equal.

Say for Example of

a b 1 2

c d 3 4

   =

      

then a = 1, b = 2, c = 3, d = 4

Scalar multiplication of a matrix

If a scalar quantity (say k) multiply by a matrix A of order m x n, then k is multiply by each element of matrix

A.

i.e. kA = kaij where A = aij