Introduction of Operations on Matrices

The sales figure of two car dealers during January 2013 showed that dealer A sold 5 deluxe, 3 premium and 4 standard cars, while dealer B sold 7 deluxe, 2 premium and 3 standard cars. Total sales over the 2 month period of January-February revealed that dealer A sold 8 deluxe 7 premium and 6 standard cars. In the same 2 month period, dealer B sold 10 deluxe, 5 premium and 7 standard cars. Write 2 × 3 matrices summarizing sales data for January and 2-month period for each dealer.

Construct a 3 × 4 matrix A = [a_ij] whose elements a_ij are given by:

`a_(ij)=1/2= -3i + j `

Construct a 2 × 2 matrix whose elements a_ij are given by:

`a_(ij)=e^(2ix) sin (xj)`

Construct a 4 × 3 matrix whose elements are

 a_ij = i 

Write the element a₂₃ of a 3 ✕ 3 matrix A = (a_ij) whose elements a_ij are given by `a_(ij)=∣(i−j)/2∣`