A shopkeeper has 3 varities of pens ‘A’, ‘B’ and ‘C’. Meenu purchased 1 pen of each variety for a total of ₹21. Jeen purchased 4 pens of ‘A’ variety, 3 pens of ‘B’ variety and 2 pens of ‘C’ variety for ₹60. While Shikha purchased 6 pens of ‘A’ variety, 2 pens of ‘B’ variety and 3 pens of ‘C’ variety for ₹70. Using matrix method find the cost of each pen.
Let the varieties of pen A, B and C be x, y and z respectively.
As per the Data we get,
x + y + z = 21
4x + 3y + 2z = 60
6x + 2y + 3z = 70
These three equations can be written as
A X = B
|A| = 1(9 – 4) – 1(12 – 12) + 1(8 – 18)
= 1(5) – 1(0) + 1(– 10)
= 5 – 0 – 10
= – 5
Hence, the unique solution given by x = A – 1B
C11 = (– 1)1 + 1 (9 – 4) = 5
C12 = (– 1)1 + 2 (12 – 12) = 0
C13 = (– 1)1 + 3 (8 – 18) = – 10
C21 = (– 1)2 + 1 (3 – 2) = – 1
C22 = (– 1)2 + 2 (3 – 6) = – 3
C23 = (– 1)2 + 3 (2 – 6 ) = 4
C31 = (– 1)3 + 1 (2 – 3) = – 1
C32 = (– 1)3 + 2 (2 – 4) = 2
C33 = (– 1)3 + 3 (3 – 4) = – 1
Adj A = 
X = A – 1 B = 
X = 
X = 
= 
= 
Hence, A = Rs 5, B = Rs 8 and C = Rs 8