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# RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.3) Exercise 5.3

Last updated date: 17th May 2024
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## RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.3) Exercise 5.3 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices Exercise 5.3 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 5 - Algebra of Matrices Ex 5.3 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

## Algebra Of Matrices- Chapter 5, Mathematics (Class 12)

‘Algebra of Matrices’ is the 5th chapter of class 12 mathematics. It is mainly the branch of mathematics that deals with the vector spaces between different dimensions. A matrix (plural- matrices) can be defined as an arrangement of numbers, expressions, or symbols in a rectangular array which are in rows and columns having an order of no. of rows x number of columns.

Algebra of matrix includes all the operations of matrices, such as addition, subtraction, and multiplication. There are certain rules that are needed to be followed while doing these operations.

### Some Of The Tips To Be Perfect In Algebra

• Know the basic arithmetic thoroughly.

• Get yourself convenient with negative numbers.

• Follow the step so that you will not go wrong.

• Be thorough with the formulas you use.

• Practice as much as possible.

• Take multiple mock tests so you are able to solve a variety of problems.

• Revise regularly.

• Make note of all the formulas and read them every day.

• Once the completion of the syllabus solves the previous year’s paper.

• Improve to manage time well.

• Solve the problems quickly and correctly.

## FAQs on RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.3) Exercise 5.3

1. What are matrices?

Matrices can be defined as a rectangular array of numbers real or complex. A matrix has m number of rows and n numbers of columns.  For the representation of matrices brackets i.e. [] or () are used. We can understand this with the example of a row matrix (also called row vector) which consists of a single row. They are written as [a1 a2 a3 ………. an] or [1, 7, 15].

2. How do we add or subtract matrices?

Suppose there are 2 matrices X and Y in the same order. For the addition of these two matrices it can be done by X + Y. Again, for the subtraction of these matrices, you can simply subtract the corresponding elements.

Thus, if X = (xij) m × n and Y = (yij) m × n, then X + Y = (xij + yij) m × n

3. What are the properties of multiplying two matrices?

The properties of multiplication are as follows:

• Multiplication of matrix is not commutative that is, XY ≠ YZ.

• Multiplication of matrix is associative i.e. (XY) Z = X (YZ)

• (X + Y) Z = XZ + YZ and also, X(Y+Z) = XY +XZ

• When XY=XZ then Y=Z, if it is an invertible matrix i.e. the matrix, has invertible functions given it satisfies the required conditions.

• If there are two non-zero matrices then the product of these two will be non-zero too.

4. Is this chapter important for the IIT JEE exam?

Yes, for the proper guidance and knowledge of the weightage of marks that this chapter may carry for your entrance examinations, you may talk to the Vedantu subject experts. You can get a proper guide of how and what you should study and how you can retain it without any stress. They are experts who can help you solve questions from previous years, sample papers and all other questions that are necessary for cracking IIT JEE (Prelims & Mains).

5. Can experts solve doubts that are not from the NCERT book?

Yes. There are subject-based experts who are actively working for the benefit of students and they have years of experience in teaching. The tutors of Vedantu will help you with your doubts and also explain the solution if you do not understand it. All of this will be free of cost to make learning even better. Furthermore, you can also download the study materials online which you can use for reference or in ways that might be helpful for you during studies.