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Edited By Kuldeep Maurya | Updated on Jan 20, 2022 01:22 PM IST

The RD Sharma books are the most recommended solutions for the class 12 students. The majority of the students find it hard to maintain a good consistency in scoring marks in mathematics. Even though a few chapters like the 4th Chapter Algebra of matrices, the twists and other complexities present make the students perplexed. It is highly recommended for them to use the RD Sharma Class 12th VSA book.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 4 - Algebra of Matrices Ex 4.1
- Chapter 4 - Algebra of Matrices Ex 4.2
- Chapter 4 - Algebra of Matrices Ex 4.3
- Chapter 4 - Algebra of Matrices Ex 4.4
- Chapter 4 - Algebra of Matrices Ex 4.5
- Chapter 4 - Algebra Matrices Ex FBQ
- Chapter 4 - Algebra Matrices Ex MCQ

Algebra of Matrices Exercise Very Short Asnwer Question 1

is a matrix

So, here, ’s column (i=n) is equal to ’s row(j=n) So, can be exist.

Its order is order.

Algebra of Matrices Exercise Very Short Asnwer Question 2

**Answer:** is a matrix

is a matrix**Hint: **To solve this type of question, we must know the basics of matrix multiplication.**Given:****Solution:** Here, is matrix is matrix

So, should have order

and should have order

Here A has 2 number of column and B has 2 number of row

Algebra of Matrices Exercise Very Short Asnwer Question 4

**Answer:****Hint:** Here , we use basic concept of matrix transpose.**Given:****Solution:**

Here multiplication is possible.

So,

Example

,

So, now AB must be null

Algebra of Matrices Exercise Very Short Asnwer Question 6

Algebra of Matrices Exercise Very Short Asnwer Question 8

So,

because

Algebra of Matrices Exercise Very Short Asnwer Question 10

So,

Note: To solve this type of question, must care about matrix multiplication rule.

Note: Whenever you solve the matrix multiplication’s question must follow their rules.

Algebra of Matrices Exercise Very Short Asnwer Question 16

Here, multiplication rules are followed

Let

Let

So,

So,

So,

So, Let

So, Here

So, is skew symmetric

Algebra of Matrices Exercise Very Short Asnwer Question 20

Let is matrix

So,

So,

So, here we can say thatis symmetric matrix

Write value of

Where denotes row

J denotes column

Here is skew symmetric

So,

So, if

So,

Algebra of Matrices Exercise Very Short Asnwer Question 22

Now,

Algebra of Matrices Exercise Very Short Asnwer Question 23

Both must be commutative to each other

is symmetric then

→So, let AB can be symmetric

From equation (i) and (ii)

→So, condition is matrix must be commutative and

Algebra of Matrices Exercise Very Short Asnwer Question 24

is skew symmetric or symmetric matrix

is Skew symmetric

So,

So,

Let take transpose

So, we clearly see that it satisfy the condition of skew symmetric

So, is skew symmetric matrix

4 Algebra of Matrices Exercise Very Short Asnwer Question 25

So,

So, ……(i)

Let and take transpose of it

Then

So, is symmetric matrix

4 Algebra of Matrices Exercise Very Short Asnwer Question 26

So,

4 Algebra of Matrices Exercise Very Short Asnwer Question 27

So,

Algebra of Matrices Exercise Very Short Asnwer Question 28

(is a skew symmetric matrix)

As the same sequence will be continue ,so it can be written in general term as

So, n is even.

So here is skew symmetric matrix

Algebra of Matrices Exercise Very Short Asnwer Question 30

……(i)

……(ii)

Let and take transpose

[From eqn(i) and (ii)]

So, is skew symmetric matrix

Algebra of Matrices Exercise Very Short Asnwer Question 31

For example,

(is symmetric matrix)

(is skew symmetric matrix)

So, a skew symmetric or symmetric matrix can be a square matrix’s.

Example is,

Here, and

Here we find and

Note: We must use the union algebra concept of matrix.

Algebra of Matrices Exercise Very Short Asnwer Question 33

Here,

.......(i)

.........(ii)

[From (i) and (ii)]

RHS=LHS

So,

Here,Both side has matrix

So we can write

.....(i)

[From (i)]

Algebra of Matrices Exercise Very Short Asnwer Question 35

Here,Both side has matrix

So we can write

......(i)

[From (i)]

Algebra of Matrices Exercise Very Short Asnwer Question 36

Here, Both side has matrix

So we can write

...(i)

.....(i)

=RHS

Algebra of Matrices Exercise Very Short Asnwer Question 37

=Here both sides coloumn and row is similar.So,let's use matrix multiplication

Algebra of Matrices Exercise Very Short Asnwer Question 38

Here Both side has matrix

So we ca write

.............(i)

[ y=0 from eqn (i)]

Note: You should must match the order of matrix.

Algebra of Matrices Exercise Very Short Asnwer Question 39

Let's find first

[For tranpose]

Algebra of Matrices Exercise Very Short Asnwer Question 40

Here, Both side has matrix

So we can write

.....(i)

[From eqn (i)]

So, value of a is 8.

Algebra of Matrices Exercise Very Short Asnwer Question 41

is order of matrix

is order of matrix

Find order

Here,

→So, C1 and R2 is same So, mutiplication is possible.So,A×B matrix's order is 3×3 matrix

Algebra of Matrices Exercise Very Short Asnwer Question 42

is idetnify matrix

Find

A is identity matrix A=

Algebra of Matrices Exercise Very Short Asnwer Question 43

On Comparing,

Algebra of Matrices Exercise Very Short Asnwer Question 44

is a identity matirx

is a square matrix

then find the value of

So,

Algebra of Matrices Exercise Very Short Asnwer Question 45

is written as

B+C where B is symmertric and C is skew symmetric matrix Find B

.....(i)

Algebra of Matrices Exercise Very Short Asnwer Question 46

matrix

So,

is matrix

Here, is exist

So, in

Here is exist

So, in

So, is matrix

Algebra of Matrices Exercise Very Short Asnwer Question 47

Number of elements = 4

Number of entries =

Number of possible matrices =

Algebra of Matrices Exercise Very Short Asnwer Question 48

Here both are matrix

So,

[From eqn (i)]

...(ii)

Let's check both value

LHS =

=RHS

4 Algebra of Matrices Exercise Very Short Asnwer Question 49

So, Possible order is or

Algebra of Matrices Exercise Very Short Asnwer Question 50

2×2 matrix, A=an, whose elements are given by

Here,

So,

4 Algebra of Matrices Exercise Very Short Asnwer Question 51

4 Algebra of Matrices Exercise Very Short Asnwer Question 52

Algebra of Matrices Exercise Very Short Asnwer Question 53

Here both sides has matrix

So,we can write

....1i)

.....(2)

Let's multiply (-2) with eqn (1)

Algebra of Matrices Exercise Very Short Asnwer Question 54

Here

Algebra of Matrices Exercise Very Short Asnwer Question 55

Answer:Hint: Here we use basic concept of matrix

Given: and Find

Solution:

Algebra of Matrices Exercise Very Short Asnwer Question 56

is square matrix

Algebra of Matrices Exercise Very Short Asnwer Question 57

Here both sides has 2×3matrix

Here 1st matrix has 2 columns and 2nd matrix has 2 rowsSo, multiplication is possible

4 Algebra of Matrices Exercise Very Short Asnwer Question 59

Algebra of Matrices Exercise Very Short Asnwer Question 60

(A is symmetric matrix)

(A is skew symmetric matrix)

Algebra of Matrices Exercise Very Short Asnwer Question 61

Both sides has order of matrix

So,

........(1)

...........(2)

So,

[From eqn (1) and (2)]

4 Algebra of Matrices Exercise Very Short Asnwer Question 62

4 Algebra of Matrices Exercise Very Short Asnwer Question 63

find

Here in RHS In both matrix 1st has 2 coloumn and 2nd has row

So,multiplication is possible

So, Let's do it

4 Algebra of Matrices Exercise Very Short Asnwer Question 64

is symmetric

So,

4 Algebra of Matrices Exercise Very Short Asnwer Question 65

4 Algebra of Matrices Exercise Very Short Asnwer Question 66

Here 1st has 3 columns and 2nd has 3 rows , 2nd has 3 columns and 3rd has 3 rowsSo, multiplication is possible

4 Algebra of Matrices Exercise Very Short Asnwer Question 67

Let's take tranpose of equation (1)

From eqn (1) and (2)

4 Algebra of Matrices Exercise Very Short Asnwer Question 68

**Answer:**is order of

Here in both A's column is same as B's rows

So multiplication is possible

The Chapter Algebra of matrices is not challenging for most students, yet the absence of an excellent resource to verify the answers is entirely missing. In RD Sharma Class 12th VSA 4th chapter in mathematics, the concept of matrices is dealt with in a detailed manner. These concepts include Addition, Subtraction, Multiplication of matrices, Inverse of Matrices, Transpose Matrices, Directions in Matrices using vectors, Skew matrices, Matrix Determinants, and Rank of Matrices. All these topics are asked in the RD Sharma Class 12th VSA section. There are sixty-nine questions in this section. Hence, the RD Sharma Class 12 Chapter 4 VSA solutions can be referred to.

Not only does this book help you in doing homework and assignments, but you can also use it to prepare for your public examinations. As the experts provide every solution, you can utilize this resource without any hesitation. The students might not know the limit and easy tricks to give answers for a VSA. And if they find it challenging to provide the solutions for the Very Short Answers (VSA) part, they can use the RD Sharma class 12th VSA material.

The most significant advantage is that the students need not pay even a single penny to own this book. They can download the RD Sharma Class 12 Solutions Algebra of Matrices for free from the top education website, Career360. Not only students, tutors, teachers can also make the most of this book by referring. There is an abundance of students who have benefited by using this solutions book.

As the RD Sharma books are popular among the school students and faculty members, there are high chances of questions being asked from these books at your tests and exams. And it is no surprise if you find such questions in your public exams too. Therefore, make it a practice to have the RD Sharma Class 12 Solutions Chapter 4 VSA book beside you while preparing for your exams. If you use this book, you will face no more difficulties finding the answers for the concepts in Algebra of Matrices. Visit the career 360 website and download your copy now.

**Chapter-wise RD Sharma Class 12 Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Where can I verify my VSA of Chapter 4 class 12 mathematics?

You can very well refer to the RD Sharma Class 12th VSA solutions book to cross-check or find answers for it. The answers are provided with many tricks that save your time in finding the solutions quickly.

2. Where can I get a free copy of the class 12 RD Sharma chapter 4 exercise FBQ Solutions book?

Anyone can download the RD Sharma Solution books from the Career360 website for free. All you need to do is, visit the website and search for the solutions book according to the subject and grade.

3. Is it enough to write the VSA at my public exams as given in the RD Sharma solutions book?

The experts provide the answers in the RD Sharma Class 12 Chapter 4 VSA. Hence, you can proceed to write the answers in the same way as given in the book.

4. Are the solutions given in the RD Sharma books easier for every student to understand?

The book consists of many methods of finding the solution for a mathematical question. Therefore students who are toppers as well as the average learners can explore and find the methods that they feel are easy to adapt.

5. Do the RD Sharma books follow the NCERT pattern?

Yes, the RD Sharma books follow the NCERT pattern. Hence, it becomes useful for CBSE students to use it for their exam preparations.

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