Two Trusts A and B receive Rs 70000 and 55000 respectively from central government to award prize to persons of a district in three fields of agriculture, education, and social service .Trust A awarded 10, 5,and 15 persons in the field of agriculture, education and social service respectively while trust B awarded 15,10,and 5 persons respectively. If all three prizes together amount to 6000, then find the amount of each prize by matrix method ?
the total of three prizes amount to 6000.
therefore: x+y+z = 6000..........(1)
trust A receive Rs. 70000.
therefore : 10x+5y+15z = 70000
2x+y+3z = 14000 ........(2)
trust B receive Rs. 55000/-
therefore : 15x+10y+5z = 55000
3x+2y+z = 11000 ..........(3)
therefore writing the eq(1), eq(2) and eq(3) in the form of matrices:
therefore first we will find the inverse of matrix A.
therefore x = 2000/- y = 1000/- and z = 3000/-
thus the amount of prize in the field of agriculture, education and social service are 2000/-, 1000/- and 3000/-
hope this helps you