Application of Cramer rule in daily life best example

good thing espically fo mathematics

1. Groups members Name(Roll No.) Mubashir (13) Muhammad nouman (19) Rai Amad ud din(27) Presentation topic: Cramer Rule’s and its Application

2. What is Cramer rule and it formula Cramer rule is the mathematical technique to solve the systems of Linear equations. In linear algebra , Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations. formula Ax=b

3. Applications with Example

4. Example no.1

5. Let x , y and z be the cost/scoop of Pineapple, Strawberry and Vanilla flavors, respectively. Then according to the given conditions In matrix form, we can write it as:

6. = 2(2x1-1x2) -3(3x1-5x2) +2(3x1-5x2) = 37(2x1-1x2) -3(39x1-44x2) +2(39x1-44x2) = 2(39x1-44x2) -37(3x1-5x2) +2(3x1-5x39) = 2(2x44-1x39) -3(3x44-5x39) +37(3x44-5x2) One pineapple(x)=7 Rs . One Stawbarry (y)=5Rs. One Vinilla (z)=4Rs.

7. A textile industry sells 3 brands: B 1 , B 2 and B 3 of yarn, each of which is a blend of Pakistani , Egyptian and American cotton in ratios: 1: 2 : 1 , 2 : 1 : 1 and 2 : : 2 . If cost/kg of B 1, B 2 and B 3 is Rs . 40 , 50 and 60 respectively, Example no.2 find the cost/kg of cotton of each country.

8. 1: 2 : 1 , 2 : 1 : 1 , 2 : : 2 Let x , y and z be the cost/kg of Pakistani, Egyptian and American Cotton respectively. Then according to the given conditions

9. In matrix form, we can write it as:

10. = 1(1x1-0x1) -2(2x1-1x1) +1(2x1-1x1) = 160(1x1-0x1) -2(200x1-120x1) +1(200x1-120x1) = 1(200x1-120x1) -160(2x1-1x1) +1(2x1-1x200) = 1(1x120-0x200) -2(2x120-1x200) +160(2x120-1x1)

11. According to Cramer’s Rule