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Three shopkeepers A ,\ B\ a n d\ C go to...

Three shopkeepers `A ,\ B\ a n d\ C` go to a store to buy stationary. `A` purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. `B` purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. `C` purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs. 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individuals bill.

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To solve the problem of calculating the individual bills of shopkeepers A, B, and C using matrix multiplication, we will follow these steps: ### Step 1: Define the Purchases Matrix We first need to create a matrix that represents the quantities of items purchased by each shopkeeper. Let: - A's purchases: 12 dozen notebooks, 5 dozen pens, 6 dozen pencils - B's purchases: 10 dozen notebooks, 6 dozen pens, 7 dozen pencils ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A and B are square matrices of the same order such that A B=B A ...

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  2. Let A=[1 1 1 3 3 3] , B=[3 1 5 2-2 4] and C=[4 2-3 5 5 0] . Verify tha...

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  3. Three shopkeepers A ,\ B\ a n d\ C go to a store to buy stationary....

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  4. The cooperative stores of a particular school has 10 dozen physics ...

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  5. In a legislative assembly election, a political group hired a publi...

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  7. To promote making of toilets for women, an organisation tried to ge...

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  8. There are two families A and B.In family A, there are 4 men, 6 women a...

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  9. In a parliament election, a political party hired a public relation...

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  10. The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and ...

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  11. A trust invested some money in two types of bonds. The first bond pays...

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  12. If A=[-1 2 3] and B=[-2\ \ -1\ \ -4] , verify that (A B)^T=B^T\ A^T

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  13. If A=[costheta-sinthetasinthetacostheta] , then find the values of ...

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  14. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying "AA"^T=9I3 , th...

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  15. Find the values of x,y,z if the matrix A=[[0,2y,z],[x,y,-z],[x,-y,z]] ...

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  16. Let A=[2-3-7 5] and B=[1 0 2-4] , verify that (2A)^T=2A^T (ii) (A+B)^T...

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  17. If A=[3 5 2] and B=[1\ \ 0\ \ 4] , verify that (A B)^T=B^T\ A^Tdot

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  18. Let A=[1-1 0 2 1 3 1 2 1] and B=[1 2 3 2 1 3 0 1 1] . Find A^T ,\ B^T ...

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  19. If A=[-2 4 5] , B=[1\ \ 3\ \ -6] , verify that (A B)^T=B^T\ A^T

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  20. If A=[(2, 4,-1),(-1, 0, 2)] , B=[(3, 4),(-1, 2),( 2, 1)] , find (A B)^...

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