Q. 325.0( 1 Vote )

# 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.

Answer :

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 ^{– 1}B

C_{11 =} (– 1)^{1 + 1} (9 – 4) = 5

C_{12} = (– 1)^{1 + 2} (12 – 12) = 0

C_{13} = (– 1)^{1 + 3} (8 – 18) = – 10

C_{21} = (– 1)^{2 + 1} (3 – 2) = – 1

C_{22} = (– 1)^{2 + 2} (3 – 6) = – 3

C_{23} = (– 1)^{2 + 3} (2 – 6 ) = 4

C_{31} = (– 1)^{3 + 1} (2 – 3) = – 1

C_{32} = (– 1)^{3 + 2} (2 – 4) = 2

C_{33} = (– 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

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