Q. 11

# 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.

Answer :

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 ^{– 1}B

C_{11 =} (– 1)^{1 + 1} (0 + 2) = 2

C_{12} = (– 1)^{1 + 2} (– 1 – 1) = 2

C_{13} = (– 1)^{1 + 3} (2 – 0) = 2

C_{21} = (– 1)^{2 + 1} (1 + 2) = – 3

C_{22} = (– 1)^{2 + 2} (1 – 1) = 0

C_{23} = (– 1)^{2 + 3} (– 2 – 1 ) = 3

C_{31} = (– 1)^{3 + 1} (1 – 0) = 1

C_{32} = (– 1)^{3 + 2} (1 + 1) = – 2

C_{33} = (– 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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