Question

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 1

Let the prices (per kg) of onion, wheat and rice be Rs. x, Rs. y and Rs. z, respectively then

4x + 3y + 2z = 60, 2x + 4y + 6z = 90, 6x + 2y + 3z = 70

This system of equations can be written as AX = B, where

Thus, A is non-singular. Therefore, its inverse exists. Therefore, the given system is consistent and has a unique solution given by X = A −1B

Cofactors of A are,

A11 = 12 − 12 = 0,

A12 = − (6 − 36) = 30,

A13 = 4 − 24 = − 20,

A21 = − (9 − 4) = − 5,

A22 = 12 − 12 = 0,

A23 = − (8 − 18) = 10,

A31 = (18 − 8) = 10,

A32 = − (24 − 4) = − 20,

A33 = 16 − 6 = 10