A company produces three products every day. Their production on a certain day is 45 tons . It is found that the production of third product exceeds the production of first product by 8 tonswhile the total production of first and third product is twice the production of second product . Determine the production level of each product using matrix method.

Let the production level of first product = x tons.Let the production level of second product = y tons.Let the production level of third product = z tons.So, A.T.Qx+y+z=45z=x+8 x-z=-8x+z=2y x-2y+z=0We can write it in the form of AX=B.Where , A=11110-11-21 ,X=xyz and B=45-80A=1-2-12+1-2=-60So , A is non-singular. therefore, its inverse exists.A11=-2  A12=-2 A13=-2A21=-3  A22=0    A23=3A31=-1  A32=2 A33=-1So, A-1=1Aadj A=-16-2-3-1-202-23-1X=A-1Bxyz=-16-2-3-1-202-23-145-80=-16-66-90-114=111519so, x=11 , y=15  and z=19.Production level of first product=11 tons.Production level of second product=15 tons.Production level of third product=19 tons.

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