# NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in Hindi Medium as well as English Medium free to download in PDF form or use online given below. These are updated form of NCERT Textbook Solutions for the academic year 2018-19 for CBSE and UP Board scholars. Download (Miscellaneous Exercise 3 & विविध प्रश्नावली ३) here in PDF format.

## NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise

### Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in English

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in English Medium free to download as well as use it online. Get here all the exercises of Class 12 Mathematics Chapter 3, If you need Solutions in Hindi, CLICK HERE for Hindi Medium Solutions.       ### Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in Hindi

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in Hindi Medium to study online given below or move to top of the page to download in PDF. Get here all the exercises of Class 12 Mathematics Chapter 3, Go back to English Medium Solutions.       Go Back to Top of English Medium Solutions & Hindi Medium Solutions.

#### Important Extra Questions with Answer on Matrices

1. Using matrix method, solve the system of linear equations: x – 2y = 10, 2x – y – z = 8 and – 2y + z = 7. [Answer: x = 0, y = – 5, z = – 3]
2. If A = [aij] is a 2 × 2 matrix such that aij = i + 2j, write A.
3. To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper bags, scrap books and pastel sheets made by them using recycled paper, at the rate of ₹20, ₹15 and ₹5 per unit respectively. School A sold 25 paper bags, 12 scrap books and 34 pastel sheets. School B sold 22 paper bags, 15 scrap books and 28 pastel sheets. While school C sold 26 paper bags, 18 scrap books and 36 pastel sheets. Using matrices, find the total amount raised by each school. [Answer: School A = ₹850, School B = ₹805 and School C = ₹970]
4. If A = [aij] is a square matrix such that aij = i² – j², then write whether A is symmetric or skew-symmetric.
5. Two cricket teams honoured their players for three values, excellent batting, to the point bowling and unparalleled fielding by giving x, y and z per player respectively. The first team paid respectively 2, 2 and 1 players for the above values with a total prize money of 11 lakhs, while the second team paid respectively 1, 2 and 2 players for these values with a total prize money of 9 lakhs. If the total award money for one person each for these values amount to 6 lakhs, then express the above situation as a matrix equation and find award money per person for each value. [Answer: Excellent batting = 3 lakhs, Point bowling = 2 lakhs and Fielding = 1 lakhs]