1. (a) Find a matrix A such that 4 0 17 10 1 2 0 16A [ ] [ ] =[ ] [ ]- - -[ ] [ ] Also, find A-1.

2. If A = 2 3 5 3 2 4 1 1 2 -[ ] [ ] -[ ] [ ] -[ ] , find A-1 and hence solve the system of linear equations: 2x - 3y + 5z = 11, 3x + 2y - 4z = -5; x + y - 2z = -3.

3. 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.

4. Case-Study 3: Two schools A and B want to award their selected students on the values of Honesty, Hard work and Punctuality. The school A wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to its 3, 2 and 1 students respectively with a total award money of ₹ 2200. School B wants to spend ₹ 3100 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school A). The total amount of award for one prize on each value is ₹ 1200. Using the concept of matrices and determinants,

5. Case-Study 3: Three car dealers, say A, B and C, deals in three types of cars, namely Hatchback cars, Sedan cars, SUV cars. The sales figure of 2019 and 2020 showed that dealer A sold 120 Hatchback, 50 Sedan, 10 SUV cars in 2019 and 300 Hatchback, 150 Sedan, 20 SUV cars in 2020; dealer B sold 100 Hatchback, 30 Sedan, 5 SUV cars in 2019 and 200 Hatchback, 50 Sedan, 6 SUV cars in 2020; dealer C sold 90 Hatchback, 40 Sedan, 2 SUV cars in 2019 and 100 Hatchback, 60 Sedan, 5 SUV cars in 2020. (i) Write the matrix summarizing sales data of 2019 and 2020. (ii) Find the matrix summarizing sales data of 2020. (iii) Find the total number of cars sold in two given years, by each dealer? OR (iii) If each dealer receives a profit of = 50000 on sale of a Hatchback, 100000 on sale of a Sedan and 2200000 on sale of an SUV, then find the amount of p rofit received in the year 2020 by each dealer.