question_answer 1)

The cost of 4 kg onion, 3kg wheat and 2kg rice is Rs60. The cost of 2kg onion, 4kg wheat and 6kg rice is Rs.90. The cost of 6kg onion 2kg wheat and 43kg rice is Rs.70. Find cost of each item per kg by matrix method. 

Answer:

Let the cost of onion per kg = Rs.x       cost of wheat per kg = Rs.y       and cost of rice per kg = Rs.z                According to question       4x + 3y + 2z = 60; 2x + 4y + 6z = 90; 6x + 2y + 3z = 70       The given system of equations can be expressed as AX = B, where             and             = 4(12 ? 12) ? 3 (6 ? 36) + 2 (4 ? 24)       = 0 + 90 ? 40 = 50 0       Therefore A is non-singular matrix so exists and given system has unique solution.       A11 = 0; A12 = 30; A13 = ?20         A21 = ?5; A22 = 0; A23 = 10       A31 = 10; A32 = ?20; A33 =10       adj                          Now                               On equating, we get x = 5, y = 8 and z = 8.          Cost of onion per kg = Rs.5             Cost of wheat per kg = Rs.8             Cost of rise per kg = Rs.8.