 Hi and welcome to the session. I am Deepika here. Let's discuss a question. Question says, 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 biometrics method. Let's start the solution. Let cost of 1 kg onion is equal to Rs. x. Cost of 1 kg wheat is equal to Rs. y. And let cost of 1 kg rice is equal to Rs. z. According to the question, cost of 4 kg onion plus 3 kg wheat plus 2 kg rice is equal to Rs. 60. So, we have according to the question, C y 2 z is equal to Rs. 60. Again, plus 4 y plus 6 z is equal to Rs. 90. 6 x C z is equal to Rs. 70. Now, we will solve this equation by the matrix method. The above system of equations written in the form A x is equal to B will be equal to x, y z. B will be equal to Rs. 90, 70. Now, determinant of A is equal to 4 x 12 minus 12 minus 3 x minus 36 plus 2 x 4 minus 24. This is equal to 4 x 0 minus 3 x minus 30 plus 2 x minus 20. So, we will get here 0 plus 90 minus 40 which is equal to 50. Now, we will find co-factor of each and every element of A. Now, co-factor of 4 is equal to minus 1 raised to power 1 plus 1 into 12 minus 12 which is equal to 0. Again, co-factor of 3 is equal to minus 1 raised to power 1 plus 2 into 6 minus 36 which is equal to 30. In this way, we will find the co-factor of each and every element which is as follows. Now, the matrix formed by the co-factors is equal to 0, 30 minus 20 minus 5, 0, 10, 10 minus 20, 10. Now, adjoint A is equal to transpose of this matrix formed by the co-factors which is equal to 0, 30 minus 20 minus 5, 0, 10, 10 minus 20, 10. Therefore, A inverse is equal to 1 upon determinant A into adjoint of A. This is equal to 1 over 50 into 0, 30 minus 20 minus 5, 0, 10, 10 minus 20, 10. Now, A is equal to B implies A inverse B. Therefore, our x is equal to A inverse is our 1 over 50, 0, 30 minus 20 minus 5, 0, 10, 10 minus 20, 10 into B which is equal to 60, 90, 70. So, our x is equal to 1 by 50 into 0 into 60, 0 minus 5 into 90 minus 450, 10 into 70 is plus 713 into 60. This is 1800 plus 0 minus 1400. Again, we get minus 1200 plus 900 plus 700. This is equal to 1 by 50 into 250, 400 and from here we get 400. So, this is equal to 588. This implies x, y, z is equal to 588 and on equating the corresponding elements we get x is equal to 5, y is equal to 8 and z is equal to 8. Now, in the question our x was cost of 1 kg of onion and y was cost of wheat per kg and z was cost of rice per kg. Therefore, the answer for the above system of equations is cost of per kg is equal to rupees 5 as our x is 5 and cost of wheat per kg is equal to rupees 8 as our y is equal to 8 and cost of rice per kg is equal to rupees 8 as our z is also 8. So, this is the answer for the above question. I hope the question is clear to you. Bye and have a good day.