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RD Sharma class 12th exercise FBQ can be your go-to NCERT solution when preparing for board exams. If you are in the 12th standard, you need to immediately start preparing for your exams so that you don't get overworked or stressed before you actually sit for your paper. Your paper might be quite challenging to solve but worry not as RD Sharma class 12 chapter 4 exercise FBQ will help make it easier for you.

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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 MCQ
- Chapter 4 - Algebra Matrices Ex VSA

Algebra of Matrices Excercise:FBQ

Algebra of Matrices exercise Fill in the blank question 1

(a,b) = (2,4)

We know that, here, we use the basic multiplication rules of two matrixes

A is order of a × 3 and B is order of 3 × b order of matrix.

Here, we know that matrix multiplication is possible only if number of rows in second matrix are same number of columns in first matrix, i.e. order of 1

And, the resultant matrix is order of m X p, I.e. number of rows=m and number of columns=p

So,

Here A is a × 3

B is 3 × b

And, AB is 2 × 4

So, A is 2 × 3

B is 3 × 4

So, (a,b) = (2,4)

Algebra of Matrices exercise Fill in the blank question 2

PQ is 3p

Use the basic concept of matrix multiplication.

P is 3 × n and

Q is n × p order of matrix.

Here, number of P's columns and Q's rows are same

So, multiplication is possible.

∴PQ is order of 3p

Algebra of Matrices exercise Fill in the blank question 3

x = 2 and y = 1 so, 2x + y = 2(2) + 1 = 5

Use the basic concept of symmetric matrix.

A=A

By comparing respective elements,

Algebra of Matrices exercise Fill in the blank question 4

a = 3 and b = 4.

Use basic concept of matrix multiplication

.

simplify the multiplication

Algebra of Matrices exercise Fill in the blank question 5

x = 1

Use the basic concept of identity matrix.

Find x

So, here both sides have 2 x 2 matrices

Hence, by comparing respective elements,

x = ±1

Use the basic concept of matrix multiplication

Algebra of Matrices exercise Fill in the blank question 7

B is an n x m matrix.

Use the basic concept of matrix order.

A is an m x n matrix and AB and BA are defined.

Multiplication is possible, if first matrix has same number of columns as number of rows in second matrix.

AB is defined so number of rows in B is n

BA is defined so number of columns in B is m

Hence order of matrix B is

n x m

Algebra of Matrices exercise Fill in the blank question 8

AB

Use the basic multiplication rules

Algebra of Matrices exercise Fill in the blank question 9

A

Use the basic concept of matrix multiplication.

Algebra of Matrices exercise Fill in the blank question 10

A

Use the concept of diagonal matrix.

A = diag(2,-1, 3) and B = diag(-1, 3, 2)

Algebra of Matrices exercise Fill in the blank question 11

Use the basic multiplication rules.

Algebra of Matrices exercise Fill in the blank question 12

x = 0

Use the basics of identity matrix.

Algebra of Matrices exercise Fill in the blank question 13

x = (-1) and y = (-1)

Use the basics of algebra.

So,

Algebra of Matrices exercise Fill in the blank question 14

k, a, b = (-6, -4, -9)

Given

By the comparison,

And

Also,

Algebra of Matrices exercise Fill in the blank question 15

Use the basic method of multiplication.

Calculate,

So,

Algebra of Matrices exercise Fill in the blank question 16

Order 3 x 4

Use the basic concept of order of matrix.

A is a 3 x 4 matrix and A

Let’s assume order of B is m x n

A = 3 x 4

And

A

So, m=3

Also B

So,

n = 4

Hence,

Order B is 3 x 4

Algebra of Matrices exercise Fill in the blank question 17

Use the basics of transpose and multiplication of matrix

So,

Algebra of Matrices exercise Fill in the blank question 18

F(x) F(y) = F(z)

So,

F(x) F(y) = F(z) = F(x + y)

Hence,

Algebra of Matrices exercise Fill in the blank question 19

m = q

Use the basic concept of matrix order and multiplication

BC can be find because, B's columns and C's rows are same.

BC x A can be defined as,

BC

Hence, by the Rule of matrix multiplication,

m = q

Algebra of Matrices exercise Fill in the blank question 20

Use the basic concept of identity matrix.

Since,

So,

= 16 x 2I

=16 x A

Hence

Algebra of Matrices exercise Fill in the blank question 21

Use commutative property of matrix A X B = B X A

A X B = B X A

Algebra of Matrices exercise Fill in the blank question 22**Answer:**

A = A

By comparing

x + 2 = 2x - 3

By solving, x = 5

Algebra of Matrices exercise Fill in the blank question 23

BA = AB

Use the basic concept of symmetric and skew symmetric matrix.

A and B are two skew symmetric matrixes.

A and B are two skew symmetric matrixes, then

Algebra of Matrices exercise Fill in the blank question 24

3A

Use concept of matrix order

A and B are same order of matrix.

Algebra of Matrices exercise Fill in the blank question 25

Same

Addition of two matrices is defined if and only if order of the matrix is same

Addition of matrices is defined.

Both has same order then addition is possible.

Algebra of Matrices exercise Fill in the blank question 26

Use the concept of symmetric matrix

A and B are symmetric metrices.

Since A and B are symmetric so,

A = A

So,

AB = (AB)

From equation (1), (2)

AB = BA

Algebra of Matrices exercise Fill in the blank question 27

B

Use concept of symmetric Metrix

A is symmetric

A = A

Let’s take transpose of B

B

So, B

Algebra of Matrices exercise Fill in the blank question 28

Use the basics of skew- symmetrical matrix

given

-A = A

So,

So, A

Algebra of Matrices exercise Fill in the blank question 29

A

Use the basics of symmetric matrix.

A is symmetric matrix.

Given

A is symmetric matrix.

A = A

Take cube on both sides

A

So, A

Algebra of Matrices exercise Fill in the blank question 30

kA is skew symmetric Metrix

A is skew symmetric Metrix

Since A is skew symmetric Metrix

Hence, kA is skew symmetric matrix.

Algebra of Matrices exercise Fill in the blank question 31

(AB - BA) is skew symmetric matrix

Use the concept of symmetric and skew-symmetric Metrix.

Since, A and B are symmetric.

So, (AB - BA) is skew symmetric matrix

Algebra of Matrices exercise Fill in the blank question 32

We must be aware with elementary row operations

A

So, if any one row or column has zero or all the element of a row or column is zero

So, |A| = 0

Algebra of Matrices exercise Fill in the blank question 33

zero

We must be aware with scalar and null matrix

Null matrix is the matrix of which all element are zero

If we product of any matrix by the scalar zero then it is null

Algebra of Matrices exercise Fill in the blank question 34

Rectangular

A matrix is not square matrix

If matrix is not square matrix, then it can be row matrix, column matrix or rectangular matrix

But row and column matrix is also part of rectangular matrix.

Algebra of Matrices exercise Fill in the blank question 35

skew symmetric

We must know the concept of skew symmetric matrix

let A and B are skew symmetric

It is skew symmetric matrices

Algebra of Matrices exercise Fill in the blank question 36

We must know the basic of square matrix

A and B are square matrix

If k is scalar we can remove from A

If k is scalar we can multiply with A and B separately

Algebra of Matrices exercise Fill in the blank question 37

Null matrix

We should aware with symmetric and skew symmetric matrix

which matrix is symmetric and skew symmetric matrix

Let A is symmetric and skew symmetric matrix

So,

So,

A is Null matrix

Algebra of Matrices exercise Fill in the blank question 38

Distributive

To solve this, we should know the theory of matrix algebra

Matrix multiplication is ____ over matrix addition

Matrix multiplication is distributive over matrix addition

Or

A is Null matrix

Algebra of Matrices exercise Fill in the blank question 39

-1

We must be aware with basic algebra

How we can obtain negative matrix?

we can obtain negative matrix by multiplying -1 with matrix

Algebra of Matrices exercise Fill in the blank question 40

(A

For this we can use basic concept of matrix singular

For example,

Algebra of Matrices exercise Fill in the blank question 41

For that we must aware with basic operations of matrix

Lets add both matrices,

Lets add both (iii) and (i) equation

Algebra of Matrices exercise Fill in the blank question 42

0

For this we must aware with skew symmetric matrix

So both sides have 3 x 3 matrix

So,

Algebra of Matrices exercise Fill in the blank question 43**Answer:**

3**Hint:**

For this we must aware with matrix multiplication concept**Given:****Solution:**

Here 1^{st} has 3 columns and 2^{nd} has 3 rows

So, matrix multiplication is possible

The class 12 RD Sharma chapter 4 exercise FBQ solution is based on chapter 4 of the NCERT maths book, which contains the concepts of Algebra of Matrices. RD Sharma class 12th exercise FBQ will teach you the addition, multiplication, subtraction, and division of Matrices along with types of Matrices like skew-symmetric matrix, null matrix, symmetric matrix, etc. You will find a total of 43 FBQ questions, which will test your knowledge of the entire chapter. You can use the RD Sharma class 12 solutions Algebra of Matrices ex FBQ book to solve these problems and check your understanding of the chapter.

**Here is a general list of reasons why you should trust RD Sharma class 12 solutions chapter 4 ex FBQ for your exam preparations:-**

Students and teachers in India highly recommend using NCERT solutions for exams. Ex-students who have passed their board exams have also said that they had found common questions from the book in their mathematics paper.

RD Sharma class 12th exercise FBQ solutions are drafted by experts who have mastered mathematics. This means you will find some great answers with new methods to solve questions faster.

Students can use the RD Sharma class 12 solutions Algebra of Matrices ex FBQ to solve complex maths problems at home and improve their skills through self-practice. You can compare your answers to mark yourself and try to get the wrong answers corrected.

Many students have to purchase expensive study materials for exam preparations. However, RD Sharma class 12 solutions chapter 4 ex FBQ pdf is available for free on the Career360 website and can be availed of by all students.

The RD Sharma class 12th exercise FBQ pdf is regularly updated to include the latest syllabus, corresponding to the one in the NCERT textbooks or your school textbooks. Therefore, you will be able to download the newest edition of the pdf as soon as it's out.

Teachers also find the RD Sharma class 12 solutions Algebra of Matrices ex FBQ as they can test their student's knowledge by giving them questions from the book.

**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

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