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# RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.1) Exercise 5.1

Last updated date: 27th May 2024
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## RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.1) Exercise 5.1 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices Exercise 5.1 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 5 - Algebra of Matrices Ex 5.1 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

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Competitive Exams after 12th Science

This page contains RD Sharma Solutions for Class 12 Maths Chapter 5 – Algebra of Matrices. The most important thing for students to do to have a score well in Mathematics is to solve the questions of every exercise. RD Sharma Solutions for Class 12 is prepared by a team of experts who work to the best of their abilities to help students succeed in their exams. Students who practice these solutions regularly undoubtedly improve their skills, which are essential for good results.

Algebra of Matrices is a branch of mathematics that deals with vector spaces of various dimensions. The invention of matrix algebra arose as a result of the presence of n-dimensional planes in our coordinate space.

A matrix (plural: matrices) is a rectangular array of numbers, expressions, or symbols. This layout is done in horizontal rows and vertical columns in the order of several rows x number of columns. Every point pair in a three-dimensional space represents a distinct equation with one or more solutions.

Linear Algebra is the fundamental concept or central idea of applied mathematics. For example, by reliving the rules and regulations, or Axioms, we get into a generalization of vector space, which leads to the Solution of Differential Equations via calculus.

### Matrix Algebra

Matrix algebra entails matrices' operations such as addition, subtraction, multiplication, and so on.

Let us gain a better understanding of the matrix's operation-

Two matrices can be added or subtracted if (and only if) the number of rows and columns in both matrices is the same, or the matrices are in the same order.

To add/subtract, each element of the first matrix is added/subtracted from the elements of the second matrix.

### Multiplication of Matrixes

Matrix, for example, can be multiplied twice.

(i) Scalar Multiplication

(ii) Matrix multiplication with a different matrix

Scalar Multiplication is the process of multiplying a scalar quantity by a matrix. To create a new matrix, multiply each element in the matrix by the scalar quantity.

### Matrix Algebra Rule

Matrix algebra follows some rules for addition and multiplication. Consider A, B, and C to be three distinct square matrices. A' is the inverse of A, and A-1 is the transpose of A. R is a real number, and I is the identity matrix.

Now, according to the laws of matrices:

A+B = B+A →Commutative Law of Addition

A+B+C = A +(B+C) = (A+B)+C →Associative law of addition

ABC = A(BC) = (AB)C →Associative law of multiplication

A(B+C) = AB + AC →Distributive law of matrix algebra

R(A+B) = RA + RB

Also, see here rules for transposition of matrices:

(A’)’ = A

(A+B)’ = A’+B’

(AB)’ = B’A’

(ABC) = C’B’A’

The inverse rules of matrices are as follows:

• AI = IA = A

• AA-1 = A-1A = I

• (A-1)-1 = A

• (AB)-1 = B-1A-1

• (ABC)-1 = C-1B-1A-1

• (A’)-1 = (A-1)’

### More Examples of Matrix Addition

Add the top left numbers together and write the sum in the top-left position of a new matrix.

Add the numbers in the top right and write the total in the top right.

Add the numbers in the bottom left and write the total in the bottom left.

Add the numbers in the bottom right and write the total in the bottom right.

### What is a Matrix's Determinant?

A matrix's determinant is simply a special number that is used to describe matrices for solving systems of linear equations, finding inverse matrices, and other calculus applications. It's impossible to define in plain English; it's usually defined in mathematical terms or in terms of what it can help you do. A matrix's determinant has the following properties:

• It is a true figure. Negative numbers are included.

• Determinants are only available for square matrices.

• Only matrices with non-zero determinants have an inverse matrix.

• The symbol for the determinant of a matrix A is |A|, which is also the symbol for absolute value, even though the two are unrelated.

You can find RD Sharma solutions for class 12 maths chapter 5 on Vedantu. The topic of matrices algebra and its various types are covered in this chapter. A matrix is a rectangular array of numbers that is divided into columns and rows. The left matrix, for example, has two rows and three columns, whereas the ideal matrix has three rows and two columns. Matrices are used in a variety of applications and serve as the foundation for linear algebra. Their programs include solving systems of linear equations, graph theory path-finding, and a variety of group theory programs (particularly representation theory). They're also very useful for representing linear transformations (especially rotations) and thus complicated amounts.

## FAQs on RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.1) Exercise 5.1

1. How can I do well in class 9 maths?

The only way to do well in class 9 maths is to practice. Complete all of the chapter exercises. This will enhance your problem-solving abilities as well as your speed and efficiency. Important formulas, definitions, and equations can be written down in a notebook and reviewed regularly. Solve previous year's sample papers and question papers within a time limit. This will familiarise you with the paper pattern and question type, as well as help you improve your time management skills. Revise regularly to ensure that you retain everything you've learned for a longer period.

2. Where can I find useful math study materials for class 9?

Everything you need can be found on the Vedantu app or website. These resources are created by experts in the field, and the information is accurate and dependable. Students will be able to find revision notes, important questions, question papers, and much more! There are no fees or costs associated with these study materials. All students need to do is sign in, and then they can download whatever they want in pdf format. You can benefit from these free resources, which will undoubtedly help you ace your exams.

3. Why is it necessary to study from the NCERT book in class 9?

NCERT textbooks are recommended by the CBSE board. These books adhere to the most recent CBSE syllabus. As a result, these books are sufficient for preparing for class 9 exams. It simply explains concepts. When it comes to strengthening your fundamentals, these textbooks are the best. It contains a plethora of solved examples and exercises that aid in a student's learning. The exam paper will be almost entirely based on the NCERT textbook. As a result, students are advised to thoroughly study the NCERT book.

4. Is it required to complete all of the chapter exercises?

It is always preferable to complete all of the chapter exercises because they provide practice. Math is not a subject that can be learned simply by reading or memorizing. It takes dedication and practice. After each section of the NCERT textbook, there are examples and exercises. After you've finished each section, go over the solved examples and make sure you understand them completely. Then proceed to the exercises and attempt to solve them. There is a chance that the same questions will appear in the examination, so students should practice the sums in the exercises thoroughly.

5. Why should I look into Vedantu's RD Sharma Solutions for Class 12 Maths Chapter 5?

Students should obtain Vedantu's RD Sharma Solutions for Class 12 Maths Chapter 5 for the following reasons:

• Subject experts advise students to refer to the RD Sharma textbooks because they are one of the best study materials for exams.

• Based on the student's intelligence quotient, Vedantu's experts answer all textbook questions in simple and understandable language.

• The solutions are thoroughly explained so that students can improve their time management and problem-solving skills, which are critical in exams.

• RD Sharma solutions also help you understand the exam pattern with its mock papers.