Q11 of 75 Page 8

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

Let the numbers are x, y, z


x + y + z = 45 ……(i)


Also,


Z – x = 8 ……(ii)


Again,


x + z = 2y …… (iii)



A X = B


|A| = 1(2) – 1(– 2) + 1(2)


= 6


Hence, the unique solution given by x = A – 1B


C11 = (– 1)1 + 1 (0 + 2) = 2


C12 = (– 1)1 + 2 (– 1 – 1) = 2


C13 = (– 1)1 + 3 (2 – 0) = 2


C21 = (– 1)2 + 1 (1 + 2) = – 3


C22 = (– 1)2 + 2 (1 – 1) = 0


C23 = (– 1)2 + 3 (– 2 – 1 ) = 3


C31 = (– 1)3 + 1 (1 – 0) = 1


C32 = (– 1)3 + 2 (1 + 1) = – 2


C33 = (– 1)3 + 3 (0 + 1) = 1


X = A – 1 B =


Adj A =


X =


X =


=


Hence, x = 11, y = 15 and z = 19


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