Matrix - operations

Ever had trouble remembering addition or multiplications on Matrix.

Addition

Assume you have two set of data viz



Above two tables show sales of Cars and Bikes in India and USA in all regions in both the countries.

Now suppose we want to find total sales of cars of North region of both the countries,
what will we do,
We will add the corresponding columns from both the tables i.e. 10+2 = 12
same way if we want to find the total sales of both the product in all the four regions of both the countries, we will add the corresponding columns and result will be



This is called "Addition" operation on Matrix.

Multiplication

Now suppose you have two data set viz.

1) A table showing price, costing and profits made on each item viz car and bike



2) A table showing sales of two products namely car and bike in three countries viz India, USA and UK



3) Now suppose you want to find out how much price you charged for all the products in a country say India and what it costed you and in return what profits you made in that country.

To do this we will do :
Price:
( price of car * Sale of Car in India ) + ( Price of Bike * Sale of Bike in India)
( 10 * 100 ) + ( 6 * 200 )
=1000+1200
=2200

Cost:
( cost of car * Sale of Car in India ) + ( cost of Bike * Sale of Bike in India)
( 6 * 100 ) + ( 4 * 200 )
=600+800
=1400

Profit:
( profit on car * Sale of Car in India ) + ( Profit on Bike * Sale of Bike in India)
( 4 * 100 ) + ( 2 * 200 )
=400+400
=800


same way we can find all the other variables, the result will be




This is multiplication of Matrix.