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.

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 =

X =

X =

=

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Irodov Special - Electrostatics | Strengthen Your Basics29 mins
Types of solution on the basis of Raoult's Law44 mins
Irodov Special - Electrostatics | Strengthen Your Basics (Part 2)23 mins
Buffer solution - Learn through Interactive Quiz55 mins
Functional Equations - JEE with ease48 mins
Lets get back to world of Buffer solution41 mins
Buffer solution still confuses you? Watch this session44 mins
DNA Fingerprinting42 mins
Meselson and Stahl experiment49 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses