# NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 Matrices in Hindi Medium and English Medium free to download or use online with download. All solutions are based on new CBSE Curriculum 2018-2019 for CBSE MP Board and UP Board students following NCERT Books. Download (Exercise 3.4) here in PDF or use online solutions given below.

## NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4

### Class 12 Maths Chapter 3 Exercise 3.4 Matrices in English

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 Matrices in English Medium update for the current academic session 2018-19 for UP Board and CBSE Board students. 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 Exercise 3.4 Matrices in Hindi

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 Matrices in Hindi Medium online digital contents as well as downloadable form files. 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 Answers for Practice

1. A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal. [Answer: a = 2, b = 3, No]
2. Prove that the diagonal elements of a skew-symmetric matrix are all zero.
3. Give examples of matrices (i) A and B such that AB ≠ BA. (ii) A and B such that AB = O but A ≠ O, B ≠ O. (iii) A and B such that AB = O but BA ≠ O. (iv) A, B and C such that AB = AC but B ≠ C, A ≠ O.
4. If A and B are skew symmetric matrices of the same order, prove that AB + BA is symmetric matrix.
5. Let A and B be square matrices of the same order. Does (A + B)² = A² + 2AB + B² hold? If not, why?
6. The monthly incomes of Mohan and Sohan are in the ratio 3:4 and their monthly expenditures are in the ratio 5:7. If each saves ₹15000 per month, find their monthly incomes and expenditures using matrices. [Answer: ₹90000 and ₹120000]
7. For any square matrix write whether AA’ is symmetric of skew-symmetric.
8. Three shopkeepers A, B and C go to a store to buy stationary. A purchase 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs ₹1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill. [Answer: ₹157.80, ₹167.40 and ₹281.40]