Four families decided to go watch a movie on a Friday evening. The Rahmans (R) have 6 family members, the Khans (K) have 3, Sarkars (S) 2, and the Hasans (H) 2.

They buy a movie-ticket for each member. During the intermission, R goes to the concession-stand and buys 2 large popcorns. K buys 2. S and the H buy 2 and 0 respectively. Once the movie ends, the families go to an ice-cream parlour nearby. R orders 3 scoops of ice-cream and 3 coffees. K orders 1 scoops of ice-cream and 2 coffees. S orders 2 scoops of ice-cream and 0 coffees. H orders 2 scoops of ice-creams and 2 coffees.

At the end of the night, the total expenditure of the families are as follows: The Rahmans have spent Tk. 4949; the Khans have spent Tk. 2614; the Sarkars have spent Tk. 2054; and the Hasans have spent Tk. 2124.

Using the information above, convert the Friday night expenditures of the four families into a system of linear equations. Convert this system of equations into the matrix form.

-What is the determinant of the coefficient matrix?

-What is the price of a movie ticket?

-What is the price of a pop-corn?

-What is the price of a scoop of ice-cream?

-What is the price of a cup of coffee?