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RD Sharma class 12th exercise 4.1 solution is a pretty popular choice for students in NCERT solutions. Mathematics is a complex subject that needs a lot of practice. The RD Sharma class 12th exercise 4.1 will help you in this endeavor to master mathematics and ace your exams.

The class 12 RD Sharma chapter 4 exercise 4.1 solution is a highly sought-after book that students and teachers praise in the entire country. The answers in RD Sharma class 12th exercise 4.1 solution sets are crafted by experts who have mastered mathematics. In addition, you will find a variety of tips and tricks to increase your problem-solving speed.

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

- 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 VSA
- Chapter 4 - Algebra Matrices Ex MCQ

**Algebra of Matrices Exercise 4.1**

Algebra of Matrices Exercise 4.1 Question 1

Here we have to find the possible order of the given matrix

Then ordered pairs and will be be

Now, if it has 5 elements then possible orders are .

Algebra of Matrices Exercise 4.1 Question 2 (i)

and

Here we have to find out the values of

Hint:

Also given that

and

Now comparing with eqn (i) and (ii) we have,

,

Hence

This is the required answer.

Algebra of Matrices Exercise 4.1 Question 2 (i)

and

Here we have to find out the values of

Also given that

and

Now comparing with eqn(i) and (ii) we have,

Hence,

Algebra of Matrices Exercise 4.1 Question 3

And the order of matrix

Here we have to determine the order of matrices and

So,

= first row of

So, order of Matrix

Again, = second column of

Therefore, order of .

Algebra of Matrices Exercise 4.1 Question 4 (i)**Answer:** ,

Here we have to construct matrix as

Let

So, the elements in a matrix are

Substituting these values in Matrix , we get

Hence this is the required answer.

Algebra of Matrices Exercise 4.1 Question 4 (ii)

Here we have to construct matrix as

So, the elements in a matrix are

Substituting these values in Matrix , we get

Hence this is the required answer.

Algebra of Matrices Exercise 4.1 Question 4 (iii)

Here we have to construct the matrix according to

question and then construct matrix.

So, the elements in a matrix are

Substituting these values in Matrix , we get

Hence this is the required answer.

Algebra of Matrices Exercise 4.1 Question 4 (iv)

Here we have to construct the matrix according to

So, the elements in a matrix are

Substituting these values in Matrix , we get

Hence this is the required answer.

Algebra of Matrices Exercise 4.1 Question 5 (i)

Here we have to construct matrix according to

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (ii)

Here we have to construct matrix according to

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (iii)

Here we have to construct matrix according to

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (iv)

Answer:Given:

Here we have to construct matrix according to

Hint: Substitute required values in the matrix

Solution: Let

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (v)

Here we have to construct matrix according to

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (vi)

Answer:Given:

Here we have to construct matrix according to

Hint: Substitute required values in the matrix

Solution: Let

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 5 (vii)

Here we have to construct matrix according to

So, the elements in a are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 6 (i)

Here we have to construct matrix according to

Let

So,

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 6 (ii)

Here we have to construct matrix according to

Let

So,

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 6 (iii)

Here we have to construct matrix according to

Let

So,

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 6 (v)

Here we have to construct matrix according to

Let

So,

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 7 (i)

Here we have to construct matrix according to

Let

So, The elements in a matrix are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 7 (ii)

Here we have to construct matrix according to

Let

So, the elements in a matrix are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 7 (iii)

Here we have to construct matrix according to

Let

So, The elements in a matrix are

Substituting these values in Matrix , we get

Algebra of Matrices Exercise 4.1 Question 8

**Answer:** and **Given: **Here given that

We have to find the value of and **Hint:** If two matrices are equal then the elements of each matrix are also equal.**Solution:** Given that two matrices are equal

By equating them, we get

……(i)

……(ii)

……. (iii)

…….. (iv)

Multiplying equation (ii) by 2 and adding to equation (i), we get

Now substituting the value of in eqn (i), we get

Now by adding eqn(iii) and eqn (iv)

Now, again substituting the value of in eqn(iii), we get

Hence, and

Algebra of Matrices Exercise 4.1 Question 10

Here we have to find out the values of and .

Given that two matrices are equal

By equating them, we get

….. (i)

……(ii)

……(iii)

and ……(iv)

Multiplying eqn(i) by 2 and adding to eqn(ii) we get

Now, substituting the value of a in eqn(i)

Multiplying eqn(iii) by 3 and adding to eqn(iv) we get

Now, substituting the value of c in eqn(iv) we get

Hence

Algebra of Matrices Exercise 4.1 Question 11

Answer:Given:

Hint: If If two matrices are equal then the elements of each matrix are also equal.

Solution: Here

Since corresponding entries of equal matrices are equal, So

….. (i)

….. (ii)

….. (iii)

….. (iv)

….. (v)

….. (vi)

Equation (ii) gives

Putting the value of z in eqn(iv) we get

Putting the value of in eqn(v) we get

Hence

Algebra of Matrices Exercise 4.1 Question 12

We have to find the value of and

Since corresponding entries of equal matrices are equal, So

….. (i)

….. (ii)

….. (iii)

….. (iv)

Put the value of in eqn(ii) we get

Put the value of in eqn(iv) we get

Put the value of in eqn(iii) we get

Hence,

Algebra of Matrices Exercise 4.1 Question 13

We have to find the value of and

Since corresponding entries of equal matrices are equal, So

….. (i)

….. (ii)

….. (iii)

….. (iv)

Solving eqn(i) and (iii), we get

Putting the value of in eqn (i), we get

Equation (ii) and (iv) gives the values of and respectively. So,

Hence, and

Algebra of Matrices Exercise 4.1 Question 14

Here we have to find out all the values of

for and

Equating the entries, we get

; ;

Similarly,

and

and

and

Lastly,

Hence,

Algebra of Matrices Exercise 4.1 Question 15

Here we have to calculate the value of

The corresponding entries of equal matrices are equal, So

Case 1: If and

Case 2: If and

Hence or

Algebra of Matrices Exercise 4.1 Question 16

Here we have to find the value of

The corresponding entries of equal matrices are equal, So

….. (i)

….. (ii)

….. (iii)

….. (iv)

From equation (ii) and (iii) we get

and

From eqn (iv) we have,

Substituting the value of in eqn (i), we get

Substituting the value of in eqn (i), we get

Hence value of are and respectively

Algebra of Matrices Exercise 4.1 Question 17 (i)

Order of row matrix =

Order of column matrix =

So, order of a row as column matrix =

Hence required matrix =

Algebra of Matrices Exercise 4.1 Question 17 (ii)

Here we have to give an example of diagonal matrix which is not scalar

So, a diagonal matrix which is not scalar must have and for .

Hence Required matrix =

Algebra of Matrices Exercise 4.1 Question 17 (iii)

Here we have to create an example of triangular matrix.

such that for

Hence required matrix

Algebra of Matrices Exercise 4.1 Question 18

and

Here we have to write summarizing sales data.

Solution: Given data is

For January 2013:

Hence,

And For January – February:

Hence,

Algebra of Matrices Exercise 4.1 Question 19

Answer: and are not equal for any value of

Given: and

We have to find out the value of and

Hint: We will use equality of matrices.

Solution: Here

Since equal matrix have all corresponding entries equal. So,

….. (i)

….. (ii)

….. (iii)

Solving equation (i), We get

Solving equation (ii), We get

Here

So, there is no real value of from equation (ii)

Solving equation (iii), We get

From solution of equation (i) (ii) and (iii)

we can say that and cannot equal for any value of

Algebra of Matrices Exercise 4.1 Question 20

We have to find out the value of and

Since, corresponding entries of equal matrices are equal. So,

….. (i)

….. (ii)

….. (iii)

Solving equation (i), We get

Solving equation (ii), We get

Solving equation (iii), We get

From equation (ii) and (iii)

We have common value of

So,

Algebra of Matrices Exercise 4.1 Question 21

We have to find out the value of and

Corresponding elements of two equal matrix are equal.

….. (i)

….. (ii)

….. (iii)

Solving equation (i), We get

Solving equation (ii), We get

Solving equation (iii), We get

Here, we have common value of from equation (ii) and (iii)

Hence,

The class 12 RD Sharma chapter 4 exercise 4.1 solution contains the chapter Algebra of Matrices which explores Order of the matrix, Matrix formation, addition, subtraction, multiplication, etc., of matrices along with types of Matrices like null matrices, diagonal Matrices, and triangular matrices. Exercise 4.1 contains 39 questions including subparts, on two levels based on these concepts.

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Download E-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

1. What are the benefits of using RD Sharma class 12th exercise 4.1 Solutions?

RD Sharma class 12th exercise 4.1 Solutions can be extremely helpful to students who will be appearing for their board exams. In addition, students can use these answers to test their knowledge at home and develop their math skills.

2. What does the 4th chapter of the Class 12 Mathematics book contain?

The 4th chapter of the book contains advanced concepts and problems on matrices. For example, there will be sums on addition, subtraction, division, and multiplication of matrices. You will also explore types of Matrices like skew-symmetric matrix, null matrix, symmetric matrix, etc.

3. Who can use class 12 RD Sharma chapter 4 exercise 4.1 solution?

The class 12 RD Sharma chapter 4 exercise 4.1 solution can be used by students, teachers, and parents. Students can use these solutions to practice at home. Teachers can use RD Sharma class 12 chapter 4 exercise 4.1 to give homework to students and mark their performance. Parents can also similarly use these books to help their children test themselves at home.

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You will be able to download the class 12 RD Sharma chapter 4 exercise 4.1 solution book from Career360 at no cost.

5. Does RD Sharma class 12 solutions Algebra of Matrices ex 4.1 have the updated syllabus?

The RD Sharma class 12 solutions Algebra of Matrices ex 4.1 books will have an updated syllabus if you download the newest version of their free pdf.

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