Problem 16 Easy Difficulty

The cost of $4 \mathrm{~kg}$ onion, $3 \mathrm{~kg}$ wheat and $2 \mathrm{~kg}$ rice is $\mathrm{Rs} 60$. The cost of $2 \mathrm{~kg}$ onion. $4 \mathrm{~kg}$ wheat and $6 \mathrm{~kg}$ rice is $\mathrm{Rs} 90$. The cost of $6 \mathrm{~kg}$ onion $2 \mathrm{~kg}$ wheat and $3 \mathrm{~kg}$ rice is $\mathrm{Rs} 70$. Find cost of each item per $\mathrm{kg}$ by matrix method.

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 4

Determinants

Section 6

Adjoint and Inverse of a Matrix

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Problem 16

Video Transcript

Hello. We have number 16. And the question is being given and this is basically what problem. And we need to use the metrics method to solve it. Given that cost of four K Joanie and three crazy. So basically costs are given. So we have to assume that led access the cost of cost of onion. Why is the cost of uh of it? And that is the cost Of Of course, of course of 30s rice and this all our by Katie. So according to the question given data, we can be we have four Kz of onion. So four X. Similarly it will be three Y plus two. That the total cost is 60 two x plus four y plus six zero. Total cost is 90 and six X plus two while was treated total cost is 70. So these are the three questions and we want to solve it. So this could be expressed in terms of X equal to be where mm we can write a as The coefficient matrix 4-6342 And to six and 3. This is X Y zed and B is 60 90 and 17. Okay, this is 19 90. But now this we have a. So since we need to find the value of this so we know that X will be equal to from here, X will be equal to a inverse being. So we have to find a inverse first For that. Let us get a which is 4-6,342, 263. And a inverse is always one by a determinant into a joint of a and a joint of his transporter of the spectrum metrics of a. So before doing anything will be first finding the determinant mm So for 12 -12 -3 6936 plus two, uh 4 -24. So this will become zero plus 90 and minus 40. That is 50, which is not equal to zero. So the universe is possible. Let's start finding the Co factors. Okay, the victors A 11 for Co factor will be starting with plus minus plus minus plus minus plus. That is alternative sign of minus. And plus co factor of four will be plus sign. The determinant of these four things. These four elements. Similarly, we'll be finding out each and every Cool factor Plus positive sign. It will be 12 -12. Uh Okay, so Yes, -1il. Very good. 12 -12. That is zero. A 12 will be equal to uh negative sign of course. And this is six minus statistics, That is 30 A 13 will be with a plus sign blessed and four minus 24 That is -20 A 21 will be with negative sign. So 9 -4 that is -5. A 22 will be placed 12 -12 that is zero. A 23 building with a minus sign eight minus 18 at 10 and 831 will be with positive sign 18 -8 that is 10 A 32 will be with a negative sign 24 -4 -20 and a 33 will be with positive saying 16 -6 that is 10. So we have yes so victor all the co victors. So it joint it will be Transporter of Kovykta metrics that is 0 -5 then 30 0 -20 and -20 then and 10 is transposed that is zero 30 minus 20 And -50 then and 10 -20 and 10. This is transporter of transport co victim mattress physical bakery too. The it giant. Okay so A. X. Becomes equal to tax becomes equal to a universe be so universe will be one x 50 and all this 0 -5 10 30 -20 And -2010. And then. No it was big. This is the universe and B. We have 60 90 and 70. So this will be one by 50 zero -40-57. And did That 250 and 400 and 400. So if you multiply with no X. X. Why zet 250 x 50 50 458 8 458. This is five story. Okay so we have X. Equal to five Y. equal to eight That equal to eight. So cost of onion phone in fiber people K. G. Cost of wheat A two page per kg. And cost cost of rice is eight kg. So they should be the answer. Thank you.

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