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

## 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 [a_{1} a_{2} a_{3} ………. a_{n}] 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 = (x_{ij}) m × n and Y = (y_{ij}) m × n, then X + Y = (x_{ij} + y_{ij}) 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.