A company produces three products every day Their production on a certain day is 45 tons It - Maths - Matrices

Question

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

Rishabh Mittal · Accepted Answer

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=-6≠0So , 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