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.
Solution
Let the cost of onion, wheat and rice per kg. be Rs. ,v, Rs. y and Rs. r respectively.
From given conditions,
4x + 3y + 2z = 60
2x + 4y + 6z = 90
6x + 2y + 3z = 70
These equations can be written as
Co-factors of the elements of first row of | A | are
i.e. (12 – 12), – (6 – 36), (4 – 24) i.e. 0, 30, – 20 respectively.
Co-factors of the elements of second row of | A | are
i.e. – (9 – 4), (12 – 12), – (8 - 18) i.e. – 5, 0, 10 respectively.
Co-factors of the elements of third row of | A | are
i.e. (18 – 8), – (24 – 4), (16 – 6), i.e. 10, – 20, 10 respectively.
∴ the cost of onion, wheat and rice per kg. are Rs. 5, Rs. 8, Rs. 8 respectively.
