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Edited By Ramraj Saini | Updated on Dec 03, 2023 03:39 PM IST | #CBSE Class 12th

**NCERT Solutions for Exercise 3.2 Class 12 Maths Chapter 3 Matrices **are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the **latest syllabus and pattern of CBSE 2023-24. **NCERT solutions for class 12 maths chapter 3 exercise 3.2** **consist of questions related to operations on matrices like the addition of matrices, multiplication of a matrix by a scalar, properties of matrix addition, and properties of scalar multiplication of a matrix. Topics such as properties of multiplication of matrices like associative, distributive, and existence of multiplicative identity are also covered in the NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2. There are 22 questions given in exercise 3.2 class 12 maths solutions. You can take help from these class 12 maths ch 3 ex 3.2 solutions. You are advised to solve more problems to get conceptual clarity.

**12th class Maths exercise 3.2 **answers** **are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

**Also, see**

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**Question 1(i) **Let , ,

A + B

(i) A + B

The addition of matrix can be done as follows

**Question 1(iii) **Let , ,

3A - C

(iii) 3A - C

First multiply each element of A with 3 and then subtract C

**Question 2(ii). **Compute the following:

(ii) The addition operation can be performed as follows

**Question 2(iii). **Compute the following:

(iii) The addition of given three by three matrix is performed as follows

**Question 3(i). **Compute the indicated products.

(i) The multiplication is performed as follows

**Question 3(ii). **Compute the indicated products.

(ii) the multiplication can be performed as follows

**Question 3(iii). **Compute the indicated products.

**Answer:**

(iii) The multiplication can be performed as follows

**Question 3(iv). **Compute the indicated products.

(iv) The multiplication is performed as follows

**Question 3(vi). **Compute the indicated products.

(vi) The given product can be computed as follows

**Question 4. **If , and , then compute (A+B) and (B-C). Also verify that A + (B - C) = (A + B) - C

, and

Now, to prove A + (B - C) = (A + B) - C

(Puting value of from above)

Hence, we can see L.H.S = R.H.S =

**Question 6. **Simplify .

The simplification is explained in the following step

the final answer is an identity matrix of order 2

**Question 7(i). **Find X and Y, if

and

(i) The given matrices are

and

Adding equation 1 and 2, we get

Putting the value of X in equation 1, we get

**Question 7(ii). **Find X and Y, if

and

(ii) and

Multiply equation 1 by 3 and equation 2 by 2 and subtract them,

Putting value of Y in equation 1 , we get

**Question 10. **Solve the equation for x, y, z and t, if

Multiplying with constant terms and rearranging we can rewrite the matrix as

Dividing by 2 on both sides

**Question 11. **If , find the values of x and y.

Adding both the matrix in LHS and rewriting

Adding equation 1 and 2, we get

Put the value of x in equation 2, we have

**Question 12. **Given , find the values of x, y, z and w.

If two matrices are equal than corresponding elements are also equal.

Thus, we have

Put the value of x

Hence, we have

**Question 14(i).** Show that

To prove:

Hence, the right-hand side not equal to the left-hand side, that is

**Question 14(ii). **Show that

To prove the following multiplication of three by three matrices are not equal

Hence, i.e. .

**Question 16. **If prove that .

First, find the square of matrix A and then multiply it with A to get the cube of matrix A

L.H.S :

Hence, L.H.S = R.H.S

i.e..

**Question 18. **If and I is the identity matrix of order 2, show that

To prove :

L.H.S :

R.H.S :

Hence, we can see L.H.S = R.H.S

i.e. .

Rs. 1800

Let Rs. x be invested in the first bond.

Money invested in second bond = Rs (3000-x)

The first bond pays 5% interest per year and the second bond pays 7% interest per year.

To obtain an annual total interest of Rs. 1800, we have

(simple interest for 1 year )

Thus, to obtain an annual total interest of Rs. 1800, the trust fund should invest Rs 15000 in the first bond and Rs 15000 in the second bond.

Rs. 2000

Let Rs. x be invested in the first bond.

Money invested in second bond = Rs (3000-x)

The first bond pays 5% interest per year and the second bond pays 7% interest per year.

To obtain an annual total interest of Rs. 1800, we have

(simple interest for 1 year )

Thus, to obtain an annual total interest of Rs. 2000, the trust fund should invest Rs 5000 in the first bond and Rs 25000 in the second bond.

The bookshop has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books.

Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively.

The total amount the bookshop will receive from selling all the books:

The total amount the bookshop will receive from selling all the books is 20160.

**Q21. **The restriction on n, k and p so that PY + WY will be defined are:

(A)

(B) k is arbitrary,

(C) p is arbitrary,

(D)

P and Y are of order and respectivly.

PY will be defined only if k=3, i.e. order of PY is .

W and Y are of order and respectivly.

WY is defined because the number of columns of W is equal to the number of rows of Y which is 3, i.e. the order of WY is

Matrices PY and WY can only be added if they both have same order i.e = implies p=n.

Thus, are restrictions on n, k and p so that PY + WY will be defined.

Option (A) is correct.

respectively. Choose the correct answer in Exercises 21 and 22.

(A)

(B)

(C)

(D)

X has of order .

7X also has of order .

Z has of order .

5Z also has of order .

Mtarices 7X and 5Z can only be subtracted if they both have same order i.e = and it is given that p=n.

We can say that both matrices have order of .

Thus, order of is .

Option (B) is correct.

**More about NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2:-**

There are 20 long answer type questions and 2 multiple-type questions are given in the NCERT Solutions for **Class 12 Maths Chapter 3 Exercise 3.2**. You should try to solve all of them on your own. Also, there are 14 solved examples given before the **NCERT textbook** exercise 3.2 Class 12 Maths. Solving these examples will help you to grasp the concepts and solve textbook questions very easily. These Class 12th maths chapter 3 exercise 3.2 examples are very descriptive with help some important definitions. There are some theorems given in the textbook. Sometimes prove of these theorems is asked in the CBSE board exams. You should look into them also.

**Also Read| ****Matrices Class 12 Maths Chapter Notes**

**Benefits of NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2:-**

- NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2 are very helpful in solving NCERT problems.
- Class 12 maths chapter 3 exercise 3.2 solutions are designed the basis of guidelines given by the CBSE on which you can rely upon.
- Only Knowing the answer is enough to get good marks but you should know how to write answers in the board exams in order to get good marks.
- Exercise 3.2 Chapter 3 Maths Solutions are prepared by experts who know how best to write in the board exams.
- You can use these class 12 maths chapter 3 exercise 3.2 solutions for reference.

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Download EBook**Comprehensive Coverage:**The solutions encompass all the topics covered in ex 3.2 class 12, ensuring a thorough understanding of the concepts.**Step-by-Step Solutions:**In this class 12 maths ex 3.2, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.**Accuracy and Clarity:**Solutions for class 12 ex 3.2 are presented accurately and concisely, using simple language to help students grasp the concepts easily.**Conceptual Clarity:**In this 12th class maths exercise 3.2 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.**Inclusive Approach:**Solutions for ex 3.2 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.**Relevance to Curriculum:**The solutions for class 12 maths ex 3.2 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

**Also see-**

- NCERT solutions for class 12 Maths
- NCERT solutions for class 12 Physics
- NCERT solutions for class 12 Chemistry
- NCERT solutions for class 12 Biology

**Subject wise NCERT Exampler solutions**

- NCERT Exemplar Solutions for Class 12th Maths
- NCERT Exemplar Solutions for Class 12th Physics
- NCERT Exemplar Solutions for Class 12th Chemistry
- NCERT Exemplar Solutions for Class 12th Biology

**Happy learning!!!**

1. Can I get free NCERT solutions for Class 12 maths?

Click here to get NCERT solutions for class 12 maths. Links for solutions to each chapters of NCERT syllabus Class 12 Mathematics is available here. All the exercise questions of NCERT textbook are covered. For more questions solve use NCERT exemplar.

2. What is the use of matrix ?

Matrix is an important tool useful in science, statistics, research, representation of data, mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, etc.

3. What is zero matrix ?

A matrix all of whose entries are zero is called a zero matrix.

4. What is equal matrix ?

Two matrices are equal matrices if the order and correspondence entities of both matrices are the same.

5. Does scalar matrix is square matrix ?

Yes, the scalar matrix is a square matrix.

6. How do you identify a scalar matrix ?

A scalar matrix is a square matrix whose all diagonal elements are equal and all other elements are zero.

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6 minHave a question related to CBSE Class 12th ?

You can use them people also used problem

Hi,

The Medhavi National Scholarship Program, under the Human Resources & Development Mission (HRDM), offers financial assistance to meritorious students through a scholarship exam. To be eligible, candidates must be between 16 and 40 years old as of the last date of registration and have at least passed the 10th grade from a recognized board. Higher qualifications, such as 11th/12th grade, graduation, post-graduation, or a diploma, are also acceptable.

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hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

**
Thank you and wishing you all the best for your bright future.
**

Hello student,

**
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
**

- No school admission needed! Register directly with CBSE. (But if you want to attend the school then you can take admission in any private school of your choice but it will be waste of money)
- You have to appear for the 2025 12th board exams.
- Registration for class 12th board exam starts around September 2024 (check CBSE website for exact dates).
- Aim to register before late October to avoid extra fees.
- Schools might not offer classes for private students, so focus on self-study or coaching.

**
Remember
**
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.

I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.

**
Good luck with your studies!
**

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