A stationery shop sells two types of pens, P and Q. On Monday, the shop sold 40 pens of type P and 25 pens of type Q for a total revenue of ₹1,675. On Tuesday, it sold 30 pens of type P and 35 pens of type Q for a total revenue of ₹1,625.
Answer the following:
a. (i) Represent the above information as a matrix equation AX=Y, clearly specifying the matrices A, X and Y.
b. (ii) Show that the matrix A is invertible by evaluating its determinant.
c. (iii) Find A−1.
d. (iv) Hence determine the selling price of one pen of type P and one pen of type Q.