A stationery shop sells pencils, pens and erasers whose individual prices are unknown. The shopkeeper advertises the following three offers:
• Offer I: 2 pencils, 3 pens and 1 eraser for ₹31.
• Offer II: 1 pencil, 2 pens and 2 erasers for ₹24.
• Offer III: 3 pencils, 1 pen and 4 erasers for ₹35.
(i) If the prices of a pencil, a pen and an eraser are ₹x, ₹y and ₹z respectively, form a system of three linear equations in x,y and z based on the above data.
(ii) Write this system in the matrix equation form AX=B, clearly specifying A, X and B.
(iii) If the determinant ∣A∣ is found to be non-zero, what does this imply about the number of possible price lists (x,y,z) that satisfy all three offers? State your answer with reason.