APPLICATION OF MATRICES

EXERCISE - A

1) The sum of three number is 6. If we multiply the third number by 2 and add the first number to the result, we get 7. By adding second and third number to three times the first number. We get 12. Using matrices find the numbers.      3,1,2

2) N amount of Rs5000 is put into three investa at the rate of interest 6%, 7% and 8% per annum respectively. The total amount income is Rs358. If the combined income from the first two investments is Rs70 more than the income from the third, find the amount of each investment by Matrix method.       1000,2200,1800

3) A mixture is to be made of three foods A, B and C. The three foods A, B, C contain nutrients P, Q, R as shown below:

            Ounces per pound of Nutrient

   Food     P    Q       R

      A        1     2       5

      B        3     1       1 

      C        4     2       1 

How to form a mixture which will have 8 ounces of P, 5 ounces of Q and 7 ounces of R?           1,1,1

4) A transport company uses 3 types of Trucks A, B and C to transport 3 types of vehicles X, Y and Z. The capacity of each truck in terms of 3 types of vehicles is given as follows:

          X      Y        Z    

A       1       3        2

B       2       2        3

C       3       2        2 

Using Matrix method , find the number of truck of each type required to transport 85, 105, and 110 vehicles of X, Y and Z types respectively.       15,20,10

5) In an engineering workshop there are 10 machines for drilling, 8 machines for turning and 7 machines for grinding. Three types of bracket are made . Type I brackets require 0 minutes for drilling, 5 minutes for turning and 4 minutes for grinding. The corresponding times for type II and III brackets are 3, 3, 2 and 3, 2, 2 minutes respectively. How many brackets of each type should be produced per hour so that all the machines remain fully occupied during an hour ? Solve by using matrix method.    5,55,145

6) The sum of three numbers is 2. If twice the second number is added to the sum of the first and third, the sum is 1. By adding second and third number to five times the first number, we get 6. Find the three numbers by using matrices.     1,-1,2

7) An amount of Rs10000 is put into three investments at the rate of 10, 12 and 15% per annum . The combined income is Rs 1310 and the combined income of first and second investment is Rs190 short of the income from the third.  Find the investment in each using Matrix method.      2000,3000,5000

8) A company produces three products everyday. 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 tons while 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.     11,15,19

9) The prices of three commidity P, Q and R are Rs x, y and z per unit respectively. A purchases 4 units of R and sells 3 units of P and 5 units of Q. B purchases 3 units of Q and sells 2 units of P and 1 units of R. C purchases 1 units of P and sells 4 units of Q and 6 units of R. In the process A, B and C earn Rs6000, Rs5000 and Rs13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commidities by using matrix method.     3000,1000,2000

10) Two factories decided to award their employees for three values of 

a) adaptable to new techniques

b) careful and alert difficult situations

c) keeping calm and tense situations, at the rate of Rs x, Rs y and Rsz per person respectively . 

The first factory decided to honour respectively 2,4 and 3 employees with a total prize money of Rs29000. The second factory decided to honour respectively 5,2 and 3 employees with the prize money of Rs 30500. If the three prizes per person together cost Rs 9500, then

i) represent the above situation by a matrix equation and form linear equations using matrix multiplication.

ii) Solve these equations using Matrix.    2500,3000,4000

11) A total amount of Rs7000 is deposited in three different saving bank accounts with annual interest rates 5%, 8% and 17/2 % respectively . The total annual interest from these three accounts is Rs550 p. Equal amounts have been deposited in the 5% and 8% saving accounts . Find the amount deposited in each of the three accounts, with the help of Matrix .         1125,1125,4750

12) A shopkeeper has 3 varities of pens A, B and C.  Meenu purchased 1 pen of each variety for a total of Rs21. Jeen purchased 4 pens of varity, 3 pens of B variety and 2 pens of C variety for Rs60. While Shikha purchased 6 pens of A variety, 2 pens of B variety and 3 pens of C variety for Rs70. Using Matrix method find the cost of each pen.        5,8,8

13) Puransh has invested a part of his investment iin 10% bond A and a part in 15% bond B. His interest income during 1st year is Rs4000. If he invests 20% more in 10% bond A and 10% more in 15% bond B his income during 2nd year increases by Rs500. Find his initial investments and new investments in bonds A and B using matrix method .   I- 10000, 20000 , n-12000,22000

14) To control a crop disease it is necessary to use 8 units of chemical A, 14 units of chemical B and 13 units of chemical C. One barrel of spray P contains one unit of A,  2 units of B and 3 units of C. One barrel of spray Q contains 2 units of A, 3 units of B and 2 units of C. One barrel of spray R contents 1 unit of A, 2 units of B and 2 units of C. Using Matrix method, find how many barrels of each spray be used to just meet the requirement ?    1,2,3