# NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise 3 (Misc. Ex. 3) Matrices in Hindi Medium as well as English Medium free to download in PDF format free. Solutions are online given below for academic session 2020-21 but if you want to use offline, just download in PDF file format. UP Board and MP Board Students are also using NCERT Textbooks for their board exams. So, download UP Board Solutions and MP Board Solutions for Class 12 Maths Chapter 3 Miscellaneous from here without any charge. We have updated the NCERT Textbook Solutions for the academic year 2020-2021 for CBSE, MP Board and UP Board scholars who are using latest NCERT Books as a course books.

Download (Miscellaneous Exercise 3 or Vividh Prashnavali 3) in PDF format. All the questions are solved in videos format also. The videos related to all questions of 12 Maths Chapter 3 Miscellaneous are given just after the PDF solutions below.

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

Class: 12 | Maths (English and Hindi Medium) |

Chapter 3: | Miscellaneous Exercise |

### 12th Maths Miscellaneous Exercise 3 Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise 3 Matrices in English and Hindi Medium free to download as well as use it online given below for new academic session 2020-2021. Get all the exercises of Class 12 Mathematics Chapter 3 main page. Download NCERT Books based on latest CBSE Syllabus for new session 2020-2021. Ask your questions related to Science, Maths and other subjects in NIOS or CBSE board through discussion forum.

### Class 12 Maths Miscellaneous Exercise 3 Solutions in Hindi & English

#### Class 12 Maths Miscellaneous 3 Question 1 and 2 in Video

#### Class 12 Maths Miscellaneous 3 Question 3, 4 and 5 in Video

#### Class 12 Maths Miscellaneous 3 Question 6, 7, 8, 9 in Video

#### Class 12 Maths Miscellaneous 3 Question 10 and 11 in Video

#### Class 12 Maths Miscellaneous 3 Question 12, 13, 14, 15 in Video

#### 12th Maths Miscellaneous Ex. 3 Question 1, 2 Video in Hindi

#### 12th Maths Miscellaneous Ex. 3 Question 3, 4, 5 Video in Hindi

#### 12th Maths Miscellaneous Ex. 3 Question 6, 7, 8, 9 Video in Hindi

#### 12th Maths Miscellaneous Ex. 3 Question 10, 11 Video in Hindi

#### 12th Maths Miscellaneous Ex. 3 Question 12, 13, 14, 15 Video in Hindi

#### 12th Mahs Important 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]

##### 12th Mahs Questions from Board Papers

1. If A = [aij] is a square matrix such that aij = i² – j², then write whether A is symmetric or skew-symmetric.

2. 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]

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##### What are the properties of multiplication of matrices?

The multiplication of matrices possesses the following properties:

1. The associative law For any three matrices A, B and C. We have (AB) C = A (BC), whenever both sides of the equality are defined.

2. The distributive law For three matrices A, B and C.

(i) A (B+C) = AB + AC

(ii) (A+B) C = AC + BC, whenever both sides of equality are defined.

3. The existence of multiplicative identity For every square matrix A, there exist an identity matrix of same order such that IA = AI = A.

##### What are the properties of transpose of the matrices?

For any matrices A and B of suitable orders, we have

(i) (A′)′ = A,

(ii) (kA)′ = kA′ (where k is any constant)

(iii) (A + B)′ = A′ + B′

(iv) (A B)′ = B′ A′

##### What do you understand by the term Matrix?

A matrix is an ordered rectangular array of numbers or functions.

##### How do we find the order of a Matrix?

A matrix having m rows and n columns is called a matrix of order m × n.