Q. 164.6( 31 Votes )

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs. 70. Find cost of each item per kg by matrix method.

Class 12th NCERT - Mathematics Part-I 4. Determinants

Answer :

Let the cost of onions, wheat and rice per kg be Rs. x, Rs. y and Rs. z respectively.

Then according to the giving situation, it can be represented by a system of equations as-

4x + 3y + 2z = 60

2x + 4y + 6z = 90

6x + 2y + 3z = 70

The system of equations can be written in the form of AX = B, where

Here |A| = 4(12-12)-3(6-36) + 2(4-24) = 50 ≠ 0

Hence A^-1 will exist.

Now, A₁₁ = 0, A₁₂ = 30, A₁₃ = -20, A₂₁ = -5, A₂₂ = 0, A₂₃ = 10, A₃₁ = 10, A₃₂ = -20, A₃₃ = 10

Hence x = 5, y = 8 & z = 8.

Hence, the cost of onions is Rs. 5 per kg, the cost of wheat is Rs. 8 per kg, and the cost of rice is Rs. 8 per kg

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