CASE STUDY CHALLENGE

Matrix Algebra: Stationery Purchase Analysis

Three students, Neha, Rani, and Sam go to a market to purchase stationery items.

  • • Neha buys 4 pens, 3 notepads, and 2 erasers for ₹ 60.
  • • Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90.
  • • Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.

This system of linear equations can be solved using matrices to find the individual cost of each item.

Answer the following:

(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( AX = B \). [1]
(ii) Find \( |A| \) and confirm if it is possible to find \( A^{-1} \). [1]
(iii) (a) Find \( A^{-1} \), if possible, and write the formula to find \( X \).

— OR —

(b) Find \( A^2 – 8I \), where \( I \) is an identity matrix.

 [2]
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