The cost of 4 kg potato, 3 kg wheat and 2 kg of rice is ₹ 60. The cost of 1 kg potato, 2 kg wheat and 3 kg of rice is ₹45. The cost of 6 kg potato, 2 kg wheat and 3 kg of rice is ₹70. Find the cost of each item per kg by matrix method.
Let the price of 1kg potato, wheat and rice be x, y and z respectively.
According to the question,
4x + 3y + 2z = 60
X + 2y + 3z = 45
6x + 2y + 3z = 70
Converting into matrix form
AX = B
4R2 – R1
2R3 – 3R1
Converting back into the equations we get
4x + 3y + 2z = 60
5y + 10z = 120
- 5y = - 40
Y = 8
5×8 + 10z = 120
10z = 120 – 40
Z = 8
4x + 3×8 + 2×8 = 60
4x = 60 - 24 - 16
4x = 20
X = 5
∴ The cost of 1 kg potatoes, wheat and rice is Rs.5, Rs.8 and Rs. 8 respectively.
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