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Q.    Two cricket teams honoured their players for three values excellent batting and fielding by giving Rs. x, Rs. y, Rs. z per player respectively. The first team paid respectively 2, 2 and 1 players for the above values with a total prize money of Rs. 11 lakhs, while the second  team paid respectively 1, 2 and 2 players for these values with a total prize money of Rs. 9 lakhs. If the award money of one person each for each for these values amounts to Rs. 6 lakhs. Find the  award money per person using matrix method.

We have,money awarded to each person for excellent batting = Rs xmoney awarded to each person for excellent bowling = Rs ymoney awrded to each person for excellent fielding = Rs zNow, according to given conditions :x + y + z = 6000002x + 2y + z = 1100000x+2y+2z = 900000The above equations in matrix form can be written as :AX = Bwhere A = 111221122; X = xyz; B = 6000001100000900000Now, A = 111221122 = 14-2 - 14-1 + 14-2 = 2 - 3 + 2 = 1Let Aij be the cofactors of aij in A.Now, A11 = -124-2 = 2A12 = -134-1 = -3A13 = -144-2 = 2A21 = -132-2 = 0A22 = -142-1 = 1A23 = -152-1 = -1A31 = -141-2 = -1A32 = -151-2 = 1A33 = -162-2 = 0So, adj A = 20-1-3112-10Now, A-1 = adj AA = 20-1-3112-10Now, X = A-1B xyz =  20-1-3112-106000001100000900000 xyz = 1200000+0-900000-1800000+1100000+9000001200000-1100000+0 xyz =300000200000100000x = 300000; y = 200000; z = 100000So, money awarded to each person for excellent batting = Rs 300000money awarded to each person for excellent bowling = Rs 200000money awrded to each person for excellent fielding = Rs 100000
 

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