The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method, find the number of awardees of each category. Apart from these values, namely, honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.

Open in App

Solution

As per the information given in the question, the following equations hold true:

.

The above three equations can be represented in the form of a matrix as

Or AX = B, where,

Thus, A is non-singular. Therefore, its inverse exists.

Adj A is given by∴

Therefore, the number of awardees for Honesty, Cooperation and Supervision are 3, 4, and 5 respectively.

One more value which the management of the colony must include for awards may be Sincerity.

Suggest Corrections

Similar questions

Q. The management committee of a residential colony decided to award some of its members (say

x

) for honesty, some (say

y

) for helping others and some others (say

z

) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is

12

. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is

33

. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others using matrix category. Apart from these values namely, honesty, cooperation and supervision, suggest one more value which the management of the colony must include for awards.

Q. Workers in forts used to keep the fort neat and clean.

Can you write the algebraic expressions for these?

(i) Two added to three times a number.

(ii) Three times the sum of a number and two.

(iii) One added to the square of a number.

(iv) The square of the sum of a number and one.

(v) The sum of the third and fourth powers of a number.

(vi) The sum of the fourth powers of two numbers.

The sum of two numbers is 12. When three times the first number is added to 5 times the second number, the resultant number is 44. The two numbers are: .

Q. The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding the sum of second and third number to three times the first number, we get 12. Find the three numbers using determinants.

Join BYJU'S Learning Program