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.

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, A_{11} = 0, A_{12} = 30, A_{13} = -20, A_{21} = -5, A_{22} = 0, A_{23} = 10, A_{31} = 10, A_{32} = -20, A_{33} = 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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Determine the product and use it to solve the system of equations x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1.

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