Question

6 The sale figure of three car dealers during
March 2015 showed that dealer A solds 6 deluxe,
4 premium and 5 standard cars, dealer B solds
8 deluxe, 3 premium and 4 standard cars and
dealer C solds 4 deluxe, 2 premium and 3 standard
cars. Write 3x 3 matrices summarising sales
data for March.​

Answer 1

Given :   The sale figure of three car dealers during March 2015 showed that

dealer A solds 6 deluxe,  4 premium and 5 standard cars,

dealer B solds 8 deluxe, 3 premium and 4 standard cars and

dealer C  solds 4 deluxe, 2 premium and 3 standard  cars.

To Find :  Write 3x 3 matrices summarizing sales data for March.​

Solution:

                   Deluxe    Premium   Standard  

Dealer A         6                4                  5  

Dealer B         8                3                  4  

Dealer C         4                2                  3  

Let say X is the required matrix

Then

 $X=\left[\begin{array}{ccc}6&4&5\\8&3&4\\4&2&3\end{array}\right]$

where row represents  Dealers  

and column represent   type of cars

Matrix   A =  [ aij ]

3 * 3

aij  =  | i - j | /2

a₁₁  = | 1 - 1 | /2  =  0   , a₁₂  = | 1 - 2 | /2  =  1/2   , a₁₃  = | 1 - 3 | /2  =  1  

a₂₁  = | 2 - 1 | /2  =  1/2   , a₂₂  = | 2- 2 | /2  = 0   , a₂₃  = | 2 - 3 | /2  =  1/2  

a₃₁  = | 3 - 1 | /2  =  1   , a₃₂  = | 3- 2 | /2  =  1/2   , a₃₃  = | 3 - 3 | /2  =  0

  $A=\left[\begin{array}{ccc}0&1/2&1\\1/2&0&1/2\\1&1/2&0\end{array}\right]$

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