# 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 in PDF form or use online without download updated for new academic session 2020-2021.

All solutions are based on new CBSE Curriculum 2020-21 for CBSE MP Board and UP Board students following NCERT Books 2020-21. Download (Exercise 3.4) in PDF or use online solutions given below.## NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4

Class: | 12 |

Subject: | Maths |

Chapter 3: | Exercise 3.4 |

### 12th Maths Exercise 3.4 Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 Matrices in English Medium update for the current academic session 2020-21 for UP Board and CBSE Board students who are following the latest NCERT Books. Get all the exercises of Class 12 Mathematics Chapter 3 from main page. Share your knowledge with each other for NIOS board or CBSE Board in Discussion forum.

### Exercise 3.4 Solutions in Hindi & English

#### Important 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.

##### Questions from Board Papers

1. Let A and B be square matrices of the same order. Does (A + B)² = A² + 2AB + B² hold? If not, why?

2. 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]

3. For any square matrix write whether AA’ is symmetric of skew-symmetric.

4. 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]

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