Four families decided to go watch a movie on a Friday evening. The Rahmans (R) have 5 family members, the Khans (K) have 4, Sarkars (S) 2, and the Hasans (H) 1.

They buy a movie-ticket for each member. During the intermission, R goes to the concession-stand and buys 0 large popcorns. K buys 2. S and the H buy 2 and 2 respectively. Once the movie ends, the families go to an ice-cream parlour nearby. R orders 4 scoops of ice-cream and 1 coffees. K orders 0 scoops of ice-cream and 2 coffees. S orders 1 scoops of ice-cream and 0 coffees. H orders 0 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. 4544; the Khans have spent Tk. 3212; the Sarkars have spent Tk. 1965; and the Hasans have spent Tk. 1409.

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?